Question 1

Perform the indicated operation. Write the answer in scientific notation. -$\frac { 9.14 \times 10 ^ { 6 } } { 2 \times 10 ^ { 3 } }$ A) 9.14 x 10⁹ B) 4.57 x 10³ C) 9.14 x 10³ D) 4.57 x 10⁹

Accepted Answer

Dividing $9.14 \times 10^6$ by $2 \times 10^3$ gives $4.57 \times 10^3$ because $9.14 \div 2 = 4.57$ and $10^6 \div 10^3 = 10^{(6-3)} = 10^3$.

Question 2

Perform the indicated operation. Write the answer in scientific notation. -$\frac { 10 \times 10 ^ { - 7 } } { 2 \times 10 ^ { 4 } }$ A) 5 x 10^-11 B) 10 x 10^-11 C) 5 x 10^-3 D) 10 x 10^-3

Accepted Answer

The operation simplifies to $5 \times 10^{-11}$ by dividing the coefficients (10/2 = 5) and subtracting the exponents of 10 ($-7 - 4 = -11$).

Question 3

Simplify. Write the answer using positive exponents only.
-$\left( \frac { 4 y ^ { - 2 } } { x ^ { 6 } } \right) ^ { 2 } \left( \frac { 4 x ^ { - 6 } } { y ^ { - 1 } } \right) ^ { - 1 }$
A) $\frac { 4 x ^ { 6 } } { y ^ { 5 } }$
B) $\frac { 4 } { y ^ { 5 } }$
C) $\frac { 4 } { x ^ { 6 } y ^ { 5 } }$
D) $\frac { 4 y ^ { 5 } } { x ^ { 6 } }$

Accepted Answer

The answer of Simplify. Write the answer using positive exponents...

Question 4

Simplify. Write the answer using positive exponents only.
-$\frac { \left( 5 x y ^ { 3 } z ^ { - 3 } \right) ^ { 3 } } { \left( 2 x ^ { 5 } y z ^ { - 3 } \right) ^ { - 1 } }$
A) $\frac { 250 x ^ { 8 } y ^ { 10 } } { z ^ { 12 } }$
B) - $\frac { 125 x ^ { 8 } y ^ { 10 } } { 2 z ^ { 12 } }$
C)- $\frac { 125 y ^ { 10 } } { 2 x ^ { 2 } z ^ { 12 } }$
D) $\frac { 250 y ^ { 10 } } { x ^ { 4 } z ^ { 12 } }$

Accepted Answer

First, apply the power to each term inside the parentheses. For the numerator, $ (5^3)(x^3)(y^{3*3})(z^{-3*3}) = 125x^3y^9z^{-9} $. For the denominator, since it's raised to the power of -1, it inverts the fraction and changes the sign of the exponent, resulting in $2x^{-5}y^{-1}z^3$. Multiplying these together, you get $ \frac{125x^3y^9z^{-9}}{2x^{-5}y^{-1}z^3} = \frac{125}{2}x^{3-(-5)}y^{9-(-1)}z^{-9-3} = \frac{250x^8y^{10}}{z^{12}} $.

Question 5

Perform the indicated operation. Write the answer in scientific notation. -$\frac { 0.00027 \times 0.0002 } { 0.0009 }$ A) 6 x 10⁵ B) 54 x 10⁶ C) 54 x 10^-6 D) 6 x 10^-5

Accepted Answer

First, convert each number to scientific notation: $0.00027 = 2.7 \times 10^{-4}$, $0.0002 = 2 \times 10^{-4}$, $0.0009 = 9 \times 10^{-4}$. Then, perform the operation: $\frac{2.7 \times 10^{-4} \times 2 \times 10^{-4}}{9 \times 10^{-4}} = \frac{5.4 \times 10^{-8}}{9 \times 10^{-4}} = 6 \times 10^{-5}$.

Question 6

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\left( x ^ { 9 b + 2 } \right) ^ { 5 }$
A) $x ^ { 9 b + 10 }$
B) $5 x ^ { 9 b + 2 }$
C) $\mathrm { x } ^ { 9 b + 7 }$
D) $x ^ { 45 b } + 10$

Accepted Answer

The answer of Simplify. Assume that variables in the exponent...

Question 7

Perform the indicated operation. Write the answer in scientific notation. -$\frac { 24,000,000,000 } { 0.00006 }$ A) 18 x 10¹⁴ B) 18 x 10¹³ C) 4 x 10¹⁴ D) 4 x 10¹³

Accepted Answer

The answer of Perform the indicated operation. Write the answer...

Question 8

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\frac { 12 x ^ { 6 } a + b y 4 a - b } { - 3 x ^ { a } + 5 b _ { y } a - 2 b }$
A) $-4 x^{5} a-4 b_{y}^{3 a-3 b}$
B) $4 x ^ { 5 } a - 4 b y ^ { 3 a + b }$
C) $- 4 x ^ { 5 } a - 4 b _ { y } ^ { 3 a } + b$
D) $-4 x^{5 a}+6 b_{y} 3 a+b$

Accepted Answer

The given expression cannot be simplified directly to match any of the provided options because it contains variables and operations that do not directly cancel or simplify in a manner that matches the structure of the options given. The options seem to misunderstand or misrepresent the original expression's mathematical properties.

Question 9

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\frac { x ^ { 6 a } \left( x ^ { 6 a } \right) ^ { 7 } } { x }$
A) $x ^ { 48 a - 1 }$
B) $x ^ { 51 a - 1 }$
C) $\frac { 1 } { 48 a - 1 }$
D) $x ^ { 36 a + 1 }$

Accepted Answer

Using the rules of exponents, we first simplify the numerator: $x^{6a} \cdot (x^{6a})^7 = x^{6a} \cdot x^{42a} = x^{48a}$. Then, dividing by $x$ (which is $x^1$) gives $x^{48a-1}$.

Question 10

Simplify. Write the answer using positive exponents only.
-$\left( 5 x ^ { 6 } y ^ { 6 } \right) ^ { 2 } \left( x ^ { 8 } y ^ { 1 } \right) ^ { - 3 }$
A) $\frac { 25 } { x ^ { 12 } y ^ { 9 } }$
B) $\frac { \mathrm { y } ^ { 9 } } { 25 \mathrm { x } ^ { 12 } }$
C) $25 x ^ { 12 } y ^ { 9 }$
D) $\frac { 25 y ^ { 9 } } { x ^ { 12 } }$

Accepted Answer

To simplify the expression, apply the power of a product rule and the power of a power rule. For the first part, $(5x^6y^6)^2 = 25x^{12}y^{12}$. For the second part, $(x^8y)^{-3} = x^{-24}y^{-3}$. Multiplying these together gives $25x^{12-24}y^{12-3} = 25x^{-12}y^9$, which simplifies to $\frac{25y^9}{x^{12}}$.

Question 11

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\left( \frac { x ^ { 2 } t } { x } \right) ^ { 4 }$
A) $4 x ^ { 2 t } - 4$
B) $x ^ { 8 t - 4 }$
C) $4 x ^ { 2 t }$
D) $x ^ { 8 t }$

Accepted Answer

The answer of Simplify. Assume that variables in the exponent...

Question 12

Perform the indicated operation. Write the answer in scientific notation. -(2.2 x 10¹)³ A) 6.60 x 10⁴ B) 6.60 x 10³ C) 1.06 x 10⁴ D) 1.06 x 10⁵

Accepted Answer

The answer of Perform the indicated operation. Write the answer...

Question 13

Perform the indicated operation. Write the answer in scientific notation. -$\left( 5 \times 10 ^ { 8 } \right) \left( 4.3 \times 10 ^ { 8 } \right)$ A) 2.15 x 10⁶⁴ B) 215 x 10¹⁶ C) 21.5 x 10¹⁷ D) 2.15 x 10¹⁷

Accepted Answer

Multiplying the given numbers in scientific notation, $5 \times 4.3 = 21.5$ and $10^8 \times 10^8 = 10^{16}$. To convert $21.5 \times 10^{16}$ into proper scientific notation, it becomes $2.15 \times 10^{17}$.

Question 14

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\frac { \left( x ^ { a } + 3 \right) ^ { 6 } } { \left( x ^ { a - 4 } \right) ^ { 3 } }$
A) $3 x ^ { 7 }$
B) $x ^ { 9 a + 30 }$
C) $x ^ { 3 a + 30 }$
D) $x ^ { a } + 30$

Accepted Answer

The expression simplifies to $\left( x^a + 3 \right)^6 \cdot \left( x^{a-4} \right)^{-3}$. Using the properties of exponents, this simplifies further to $x^{6a} \cdot x^{-3(a-4)}$, which simplifies to $x^{6a} \cdot x^{-3a+12}$, resulting in $x^{3a+12}$. However, the original expression cannot be simplified in this form due to the addition inside the parenthesis, making all options incorrect. My initial explanation mistakenly applied exponent rules as if the addition inside the parenthesis could be distributed, which is not possible. Therefore, none of the provided choices accurately represents the simplification of the given expression.

Question 15

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\left( \frac { x ^ { 8 t } } { x ^ { 3 t - 6 } } \right) ^ { 3 }$
A) $3 x ^ { t + 6 }$
B) $x ^ { 15 } t + 18$
C) $3 x ^ { 15 t } - 18$
D) $x ^ { 24 t }$

Accepted Answer

The answer of Simplify. Assume that variables in the exponent...

Question 16

Perform the indicated operation. Write the answer in scientific notation. -$\frac { 10.08 \times 10 ^ { - 4 } } { 2.4 \times 10 ^ { 8 } }$ A) 4.2 x 10⁴ B) 4.2 x 10^-12 C) 8.4 x 10^-12 D) 8.4 x 10⁴

Accepted Answer

To solve $\frac { 10.08 \times 10 ^ { - 4 } } { 2.4 \times 10 ^ { 8 } }$, first divide the coefficients: $10.08 \div 2.4 = 4.2$. Then, subtract the exponents of 10: $(-4) - (8) = -12$. Thus, the answer is $4.2 \times 10^{-12}$.

Question 17

Solve. Write the answer in scientific notation. -A particle is observed moving at 9.57 x 10^-4 meters per second. Find the distance the particle would travel in 9.16 x 10^-7 seconds. A) 8.77 x 10^-11 meters B) 8.77 x 10^-10 meters C) 8.77 x 10^-9 meters D) 0.88 x 10^-10 meters

Accepted Answer

The answer of Solve. Write the answer in scientific notation.
-A...

Question 18

Perform the indicated operation. Write the answer in scientific notation. -$\left( 8 \times 10 ^ { 4 } \right) \left( 1.1 \times 10 ^ { 7 } \right)$ A) 88 x 10¹¹ B) 8.8 x 10¹¹ C) 8.8 x 10¹² D) 8.8 x 10²⁸

Accepted Answer

The answer of Perform the indicated operation. Write the answer...

Question 19

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\left( x ^ { - 2 a - 1 } \right) ^ { - 4 }$
A) $x ^ { 3 a + 3 }$
B) $\frac { 1 } { x ^ { 8 a + 4 } }$
C) $x ^ { 8 a } + 4$
D) $\frac { 1 } { x ^ { 3 a } + 3 }$

Accepted Answer

The answer of Simplify. Assume that variables in the exponent...

Question 20

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\left( x ^ { a } + 9 \right) ^ { 7 }$
A) $x ^ { a } + 63$
B) $x ^ { 7 } a + 63$
C) $x ^ { a } + 16$
D) $7 x ^ { a } + 9$

Accepted Answer

The answer of Simplify. Assume that variables in the exponent...

Quiz 1: Real Numbers and Algebraic Expressions

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 9.14 \times 10 ^ { 6 } } { 2 \times 10 ^ { 3 } }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 10 \times 10 ^ { - 7 } } { 2 \times 10 ^ { 4 } }$

Simplify. Write the answer using positive exponents only. - $\left( \frac { 4 y ^ { - 2 } } { x ^ { 6 } } \right) ^ { 2 } \left( \frac { 4 x ^ { - 6 } } { y ^ { - 1 } } \right) ^ { - 1 }$

Simplify. Write the answer using positive exponents only. - $\frac { \left( 5 x y ^ { 3 } z ^ { - 3 } \right) ^ { 3 } } { \left( 2 x ^ { 5 } y z ^ { - 3 } \right) ^ { - 1 } }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 0.00027 \times 0.0002 } { 0.0009 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( x ^ { 9 b + 2 } \right) ^ { 5 }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 24,000,000,000 } { 0.00006 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\frac { 12 x ^ { 6 } a + b y 4 a - b } { - 3 x ^ { a } + 5 b _ { y } a - 2 b }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\frac { x ^ { 6 a } \left( x ^ { 6 a } \right) ^ { 7 } } { x }$

Simplify. Write the answer using positive exponents only. - $\left( 5 x ^ { 6 } y ^ { 6 } \right) ^ { 2 } \left( x ^ { 8 } y ^ { 1 } \right) ^ { - 3 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( \frac { x ^ { 2 } t } { x } \right) ^ { 4 }$

Perform the indicated operation. Write the answer in scientific notation. -(2.2 x 10¹) ³

Perform the indicated operation. Write the answer in scientific notation. - $\left( 5 \times 10 ^ { 8 } \right) \left( 4.3 \times 10 ^ { 8 } \right)$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\frac { \left( x ^ { a } + 3 \right) ^ { 6 } } { \left( x ^ { a - 4 } \right) ^ { 3 } }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( \frac { x ^ { 8 t } } { x ^ { 3 t - 6 } } \right) ^ { 3 }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 10.08 \times 10 ^ { - 4 } } { 2.4 \times 10 ^ { 8 } }$

Solve. Write the answer in scientific notation. -A particle is observed moving at 9.57 x 10^-4 meters per second. Find the distance the particle would travel in 9.16 x 10^-7 seconds.

Perform the indicated operation. Write the answer in scientific notation. - $\left( 8 \times 10 ^ { 4 } \right) \left( 1.1 \times 10 ^ { 7 } \right)$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( x ^ { - 2 a - 1 } \right) ^ { - 4 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( x ^ { a } + 9 \right) ^ { 7 }$

Quiz 1: Real Numbers and Algebraic Expressions

Perform the indicated operation. Write the answer in scientific notation. - 9.14×1062×103\frac { 9.14 \times 10 ^ { 6 } } { 2 \times 10 ^ { 3 } }2×1039.14×106​

Perform the indicated operation. Write the answer in scientific notation. - 10×10−72×104\frac { 10 \times 10 ^ { - 7 } } { 2 \times 10 ^ { 4 } }2×10410×10−7​

Simplify. Write the answer using positive exponents only. - (4y−2x6) 2(4x−6y−1) −1\left( \frac { 4 y ^ { - 2 } } { x ^ { 6 } } \right) ^ { 2 } \left( \frac { 4 x ^ { - 6 } } { y ^ { - 1 } } \right) ^ { - 1 }(x64y−2​) 2(y−14x−6​) −1

Simplify. Write the answer using positive exponents only. - (5xy3z−3) 3(2x5yz−3) −1\frac { \left( 5 x y ^ { 3 } z ^ { - 3 } \right) ^ { 3 } } { \left( 2 x ^ { 5 } y z ^ { - 3 } \right) ^ { - 1 } }(2x5yz−3) −1(5xy3z−3) 3​

Perform the indicated operation. Write the answer in scientific notation. - 0.00027×0.00020.0009\frac { 0.00027 \times 0.0002 } { 0.0009 }0.00090.00027×0.0002​

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - (x9b+2) 5\left( x ^ { 9 b + 2 } \right) ^ { 5 }(x9b+2) 5

Perform the indicated operation. Write the answer in scientific notation. - 24,000,000,0000.00006\frac { 24,000,000,000 } { 0.00006 }0.0000624,000,000,000​

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - 12x6a+by4a−b−3xa+5bya−2b\frac { 12 x ^ { 6 } a + b y 4 a - b } { - 3 x ^ { a } + 5 b _ { y } a - 2 b }−3xa+5by​a−2b12x6a+by4a−b​

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - x6a(x6a) 7x\frac { x ^ { 6 a } \left( x ^ { 6 a } \right) ^ { 7 } } { x }xx6a(x6a) 7​

Simplify. Write the answer using positive exponents only. - (5x6y6) 2(x8y1) −3\left( 5 x ^ { 6 } y ^ { 6 } \right) ^ { 2 } \left( x ^ { 8 } y ^ { 1 } \right) ^ { - 3 }(5x6y6) 2(x8y1) −3

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - (x2tx) 4\left( \frac { x ^ { 2 } t } { x } \right) ^ { 4 }(xx2t​) 4

Perform the indicated operation. Write the answer in scientific notation. -(2.2 x 101) 3

Perform the indicated operation. Write the answer in scientific notation. - (5×108) (4.3×108) \left( 5 \times 10 ^ { 8 } \right) \left( 4.3 \times 10 ^ { 8 } \right) (5×108) (4.3×108)

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - (xa+3) 6(xa−4) 3\frac { \left( x ^ { a } + 3 \right) ^ { 6 } } { \left( x ^ { a - 4 } \right) ^ { 3 } }(xa−4) 3(xa+3) 6​

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - (x8tx3t−6) 3\left( \frac { x ^ { 8 t } } { x ^ { 3 t - 6 } } \right) ^ { 3 }(x3t−6x8t​) 3

Perform the indicated operation. Write the answer in scientific notation. - 10.08×10−42.4×108\frac { 10.08 \times 10 ^ { - 4 } } { 2.4 \times 10 ^ { 8 } }2.4×10810.08×10−4​

Solve. Write the answer in scientific notation. -A particle is observed moving at 9.57 x 10-4 meters per second. Find the distance the particle would travel in 9.16 x 10-7 seconds.

Perform the indicated operation. Write the answer in scientific notation. - (8×104) (1.1×107) \left( 8 \times 10 ^ { 4 } \right) \left( 1.1 \times 10 ^ { 7 } \right) (8×104) (1.1×107)

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - (x−2a−1) −4\left( x ^ { - 2 a - 1 } \right) ^ { - 4 }(x−2a−1) −4

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - (xa+9) 7\left( x ^ { a } + 9 \right) ^ { 7 }(xa+9) 7

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 9.14 \times 10 ^ { 6 } } { 2 \times 10 ^ { 3 } }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 10 \times 10 ^ { - 7 } } { 2 \times 10 ^ { 4 } }$

Simplify. Write the answer using positive exponents only. - $\left( \frac { 4 y ^ { - 2 } } { x ^ { 6 } } \right) ^ { 2 } \left( \frac { 4 x ^ { - 6 } } { y ^ { - 1 } } \right) ^ { - 1 }$

Simplify. Write the answer using positive exponents only. - $\frac { \left( 5 x y ^ { 3 } z ^ { - 3 } \right) ^ { 3 } } { \left( 2 x ^ { 5 } y z ^ { - 3 } \right) ^ { - 1 } }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 0.00027 \times 0.0002 } { 0.0009 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( x ^ { 9 b + 2 } \right) ^ { 5 }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 24,000,000,000 } { 0.00006 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\frac { 12 x ^ { 6 } a + b y 4 a - b } { - 3 x ^ { a } + 5 b _ { y } a - 2 b }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\frac { x ^ { 6 a } \left( x ^ { 6 a } \right) ^ { 7 } } { x }$

Simplify. Write the answer using positive exponents only. - $\left( 5 x ^ { 6 } y ^ { 6 } \right) ^ { 2 } \left( x ^ { 8 } y ^ { 1 } \right) ^ { - 3 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( \frac { x ^ { 2 } t } { x } \right) ^ { 4 }$

Perform the indicated operation. Write the answer in scientific notation. -(2.2 x 10¹) ³

Perform the indicated operation. Write the answer in scientific notation. - $\left( 5 \times 10 ^ { 8 } \right) \left( 4.3 \times 10 ^ { 8 } \right)$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\frac { \left( x ^ { a } + 3 \right) ^ { 6 } } { \left( x ^ { a - 4 } \right) ^ { 3 } }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( \frac { x ^ { 8 t } } { x ^ { 3 t - 6 } } \right) ^ { 3 }$

Perform the indicated operation. Write the answer in scientific notation. - $\frac { 10.08 \times 10 ^ { - 4 } } { 2.4 \times 10 ^ { 8 } }$

Solve. Write the answer in scientific notation. -A particle is observed moving at 9.57 x 10^-4 meters per second. Find the distance the particle would travel in 9.16 x 10^-7 seconds.

Perform the indicated operation. Write the answer in scientific notation. - $\left( 8 \times 10 ^ { 4 } \right) \left( 1.1 \times 10 ^ { 7 } \right)$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( x ^ { - 2 a - 1 } \right) ^ { - 4 }$

Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0. - $\left( x ^ { a } + 9 \right) ^ { 7 }$