Question 1

Simplify.
-$\left(\frac{b^{4}}{5}\right)^{-2}$
A) $\frac{b^{-6}}{5^{-2}}$
B) $\frac{b^{-8}}{5}$
C) $\frac{25}{b^{8}}$
D) $\frac{b^{8}}{5^{2}}$

Accepted Answer

When simplifying $\left(\frac{b^{4}}{5}\right)^{-2}$, you apply the negative exponent rule which flips the fraction and squares both the numerator and denominator, resulting in $\frac{25}{b^{8}}$.

Question 2

Simplify.
-$\left(\frac{x y^{4}}{w^{2} z}\right)^{-6}$
A) $\frac{w^{12} z^{6}}{x^{6} y^{24}}$
B) $\frac{x y^{-24}}{w^{-12} z}$
C) $\frac{x^{-6} y^{-2}}{w^{-4} z^{-6}}$
D) $\frac{x^{6} y^{-24}}{w^{-12} z^{6}}$

Accepted Answer

When you raise a fraction to a negative exponent, you invert the fraction and apply the positive exponent. Thus, $\left(\frac{x y^{4}}{w^{2} z}\right)^{-6}$ becomes $\frac{w^{12} z^{6}}{x^{6} y^{24}}$ by flipping the fraction and applying the exponent to each variable, resulting in option A.

Question 3

Write the number in scientific notation.
-158
A) $1.58 \times 10^{3}$
B) $1.58 \times 10^{1}$
C) $1.58 \times 10^{-2}$
D) $1.58 \times 10^{2}$

Accepted Answer

The number 158 can be expressed in scientific notation as $1.58 \times 10^{2}$ because moving the decimal two places to the left gives 1.58, and the exponent indicates the number of places the decimal was moved.

Question 4

Write the number in scientific notation.
-133.7
A) $1.337 \times 10^{3}$
B) $1.337 \times 10^{2}$
C) $1.337 \times 10^{-3}$
D) $1.337 \times 10^{-2}$

Accepted Answer

To express 133.7 in scientific notation, we move the decimal point 2 places to the left, which gives $1.337 \times 10^{2}$.

Question 5

Write the number in scientific notation.
-76.023
A) $7.6023 \times 10^{2}$
B) $7.6023 \times 10-2$
C) $7.6023 \times 10^{-1}$
D) $7.6023 \times 10^{1}$

Accepted Answer

The answer of Write the number in scientific notation.
-76.023
A) \(7.6023...

Question 6

Write the number in scientific notation.
-210,000
A) $2.1 \times 10^{-6}$
B) $2.1 \times 10^{6}$
C) $2.1 \times 10^{-5}$
D) $2.1 \times 10^{5}$

Accepted Answer

To convert 210,000 to scientific notation, we move the decimal point 5 places to the left, which gives us $2.1 \times 10^{5}$.

Question 7

Write the number in scientific notation.
-$17,000,000$
A) $1.7 \times 10-8$
B) $1.7 \times 10^{8}$
C) $1.7 \times 10^{-7}$
D) $1.7 \times 10^{7}$

Accepted Answer

To write $17,000,000$ in scientific notation, you move the decimal point 7 places to the left, which gives $1.7 \times 10^{7}$.

Question 8

Write the number in scientific notation.
-0.000543
A) $5.43 \times 10^{-5}$
B) $5.43 \times 10^{4}$
C) $5.43 \times 10^{-3}$
D) $5.43 \times 10^{-4}$

Accepted Answer

The answer of Write the number in scientific notation.
-0.000543
A) \(5.43...

Question 9

Write the number in scientific notation.
-0.000048612
A) $4.8612 \times 10^{-4}$
B) $4.8612 \times 10^{4}$
C) $4.8612 \times 10^{5}$
D) $4.8612 \times 10^{-5}$

Accepted Answer

To convert 0.000048612 into scientific notation, we move the decimal point 5 places to the right, making it $4.8612 \times 10^{-5}$.

Question 10

Write the number in scientific notation.
-0.000008656
A) $8.656 \times 10^{-6}$
B) $8.656 \times 10^{6}$
C) $8.656 \times 10^{-5}$
D) $8.656 \times 10^{-7}$

Accepted Answer

To convert 0.000008656 to scientific notation, we move the decimal point 6 places to the right, which gives us $8.656 \times 10^{-6}$.

Question 11

Write the number in scientific notation.
-0.000000855016
A) $8.55016 \times 10^{7}$
B) $8.55016 \times 10-6$
C) $8.55016 \times 10^{-7}$
D) $8.55016 \times 10^{6}$

Accepted Answer

To convert 0.000000855016 to scientific notation, we move the decimal point 7 places to the right, making it $8.55016 \times 10^{-7}$.

Question 12

Write the number in scientific notation.
-0.0000000234012
A) $2.34012 \times 10^{-9}$
B) $2.34012 \times 10^{-7}$
C) $2.34012 \times 10^{-8}$
D) $2.34012 \times 10^{8}$

Accepted Answer

The answer of Write the number in scientific notation.
-0.0000000234012
A) \(2.34012...

Question 13

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-The population of a small country is $3,115,000$.
A) $3.115 \times 10^{6}$
B) $3.115 \times 10^{4}$
C) $3.115 \times 10^{5}$
D) $3.115 \times 10^{-5}$

Accepted Answer

The population of $3,115,000$ can be written in scientific notation as $3.115 \times 10^{6}$, moving the decimal point 6 places to the left.

Question 14

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-A company produces 301,000 small appliances in one year.
A) $3.01 \times 10^{5}$
B) $30.1 \times 10^{4}$
C) $3.01 \times 10^{-5}$
D) $3.01 \times 10^{6}$

Accepted Answer

The number 301,000 written in scientific notation is $3.01 \times 10^{5}$, as it moves the decimal point 5 places to the left.

Question 15

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-The speed of light is $1.86 \times 10^{5}$ miles per hour.
A) $1,860,000$
B) $18,600,000$
C) 186,000
D) 0.0000186

Accepted Answer

The scientific notation $1.86 \times 10^{5}$ is equivalent to 186,000 when written without exponents.

Question 16

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-A computer can do one calculation in $1.4 \times 10^{-7}$ seconds.
A) $14,000,000$
B) 0.000000014
C) 0.000014
D) 0.00000014

Accepted Answer

The scientific notation $1.4 \times 10^{-7}$ seconds is equivalent to moving the decimal point 7 places to the left, resulting in 0.00000014.

Question 17

Convert to decimal notation.
-$7.67 \times 10^{4}$
A) 306.8
B) 7670
C) 76,700
D) 767,000

Accepted Answer

To convert $7.67 \times 10^{4}$ to decimal notation, you move the decimal point 4 places to the right, resulting in 76,700.

Question 18

Convert to decimal notation.
-$2.982 \times 10^{7}$
A) $298,200,000$
B) 208.74
C) $2,982,000$
D) $29,820,000$

Accepted Answer

To convert $2.982 \times 10^{7}$ to decimal notation, you move the decimal point 7 places to the right, resulting in $29,820,000$.

Question 19

Convert to decimal notation.
-$3.9739 \times 10^{5}$
A) $3,973,900$
B) 198.695
C) 397,390
D) 39,739

Accepted Answer

To convert $3.9739 \times 10^{5}$ to decimal notation, you move the decimal point 5 places to the right, resulting in 397,390.

Question 20

Convert to decimal notation.
-$6.19 \times 10^{-4}$
A) $-619,000$
B) 0.0000619
C) 0.000619
D) 0.00619

Accepted Answer

The expression $6.19 \times 10^{-4}$ means moving the decimal point 4 places to the left, resulting in 0.000619.

Quiz 10: Polynomials: Operations

Simplify. - $\left(\frac{b^{4}}{5}\right) ^{-2}$

Simplify. - $\left(\frac{x y^{4}}{w^{2} z}\right) ^{-6}$

Write the number in scientific notation. -158

Write the number in scientific notation. -133.7

Write the number in scientific notation. -76.023

Write the number in scientific notation. -210,000

Write the number in scientific notation. - $17,000,000$

Write the number in scientific notation. -0.000543

Write the number in scientific notation. -0.000048612

Write the number in scientific notation. -0.000008656

Write the number in scientific notation. -0.000000855016

Write the number in scientific notation. -0.0000000234012

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The population of a small country is $3,115,000$ .

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -A company produces 301,000 small appliances in one year.

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The speed of light is $1.86 \times 10^{5}$ miles per hour.

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -A computer can do one calculation in $1.4 \times 10^{-7}$ seconds.

Convert to decimal notation. - $7.67 \times 10^{4}$

Convert to decimal notation. - $2.982 \times 10^{7}$

Convert to decimal notation. - $3.9739 \times 10^{5}$

Convert to decimal notation. - $6.19 \times 10^{-4}$

Quiz 10: Polynomials: Operations

Simplify. - (b45) −2\left(\frac{b^{4}}{5}\right) ^{-2}(5b4​) −2

Simplify. - (xy4w2z) −6\left(\frac{x y^{4}}{w^{2} z}\right) ^{-6}(w2zxy4​) −6