Question 1

Simplify.&#10;

Accepted Answer

To simplify, apply the power of a product rule $(a^m)^n = a^{mn}$ and the product of powers rule $a^m \cdot a^n = a^{m+n}$ for each variable: $x^{6*3 + 8*5} = x^{18+40} = x^{58}$, $y^{8*3 + 9*5} = y^{24+45} = y^{69}$, $z^{8*3 + 5*5} = z^{24+25} = z^{49}$.

Question 2

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

When dividing exponents, you subtract the exponent in the denominator from the exponent in the numerator. So, $\mathrm { z } ^ { 35 } \div \mathrm { z } ^ { 5 }=\mathrm { z } ^ { 35-5}=\mathrm { z } ^ { 30 }$.

Question 3

Simplify.&#10;

Accepted Answer

When simplifying $\left( 10 x ^ { 3 } \right) ^ { 3 }$, you raise both the coefficient (10) and the variable with its exponent (x^3) to the power of 3. Thus, $10^3 = 1000$ and $(x^3)^3 = x^{3*3} = x^9$, resulting in $1000 x^9$.

Question 4

Simplify.&#10;

Accepted Answer

When you raise an exponent to another exponent, you multiply the exponents. Therefore, $\left( x ^ { 6 } \right) ^ { 3 } = x ^ { 6 \cdot 3 } = x ^ { 18 }$.

Question 5

Simplify.&#10;

Accepted Answer

When simplifying $\left( x ^ { 3 } \right) ^ { 6 } \left( x ^ { 2 } \right) ^ { 5 }$, use the rule $a^{m}a^{n} = a^{m+n}$ and $(a^{m})^{n} = a^{mn}$. Thus, $x^{3*6} * x^{2*5} = x^{18} * x^{10} = x^{18+10} = x^{28}$.

Question 6

Simplify.&#10;

Accepted Answer

When raising a power to another power, multiply the exponents. So, 
$$\left( 3 x ^ { 4 } y ^ { 2 } \right) ^ { 3 }=3^3 \cdot x^{4\cdot3} \cdot y^{2\cdot3}=27x^{12}y^6.$$
Therefore, the answer is choice D.

Question 7

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 8

Simplify.&#10;

Accepted Answer

When multiplying powers with the same base, you add the exponents. So, $5^5 \cdot 5^5 = 5^{5+5} = 5^{10}$. Calculating $5^{10}$ gives $9,765,625$.

Question 9

Simplify.&#10;&#10;-2^ 3* 2&#10;&#10;A) 16&#10;B) 32&#10;C) 4&#10;D) 8&#10;

Accepted Answer

To simplify the expression 2^3 * 2, we first need to calculate the value of 2^3, which means 2 raised to the power of 3.

Question 10

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

When we divide variables with the same base, we subtract the exponents. Therefore, $\frac { x ^ { 6 } } { x ^ { 4 } }$ can be simplified as $x^{6-4}=x^2$.

Question 11

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 12

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 13

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 14

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 15

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 16

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 17

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 18

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 19

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 20

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 21

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_d43a_8c7b_5b59231f15de_TB6360_00...

Question 22

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_d43c_8c7b_4342285988eb_TB6360_00...

Question 23

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_8612_8c7b_f154fa3cac79_TB6360_00...

Question 24

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_ad26_8c7b_15b556023228_TB6360_00...

Question 25

Find the missing factor or exponent(s).&#10;

Accepted Answer

The answer of Find the missing factor or exponent(s).&#10; ...

Question 26

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 27

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_8614_8c7b_37ef3412cbe5_TB6360_00...

Question 28

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_d43d_8c7b_738409e8e6b6_TB6360_00...

Question 29

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_ad29_8c7b_e5f6288c2576_TB6360_00...

Question 30

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 31

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_8613_8c7b_a16554dd2736_TB6360_00...

Question 32

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 33

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_8615_8c7b_d5b2cbcaaec7_TB6360_00...

Question 34

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 35

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_ad27_8c7b_73709a96971e_TB6360_00...

Question 36

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 37

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 38

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_d43b_8c7b_792462511dd9_TB6360_00...

Question 39

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Accepted Answer

The answer of 11eb4ae2_ed2d_5f00_8c7b_ff81a2acb614_TB6360_00 11eb4ae2_ed2d_5f01_8c7b_9594f782cde0_TB6360_0011eb4ae2_ed2d_ad28_8c7b_a959d3a7e970_TB6360_00...

Question 40

Simplify. (Assume all variables are nonzero.)&#10;

Accepted Answer

The answer of Simplify. (Assume all variables are nonzero.)&#10; ...

Question 41

Find the missing factor or exponent(s).&#10;

Accepted Answer

The answer of Find the missing factor or exponent(s).&#10; ...

Question 42

Find the missing factor or exponent(s).&#10;

Accepted Answer

The answer of Find the missing factor or exponent(s).&#10; ...

Question 43

Evaluate the given function.&#10;

Accepted Answer

The answer of Evaluate the given function.&#10; ...

Question 44

Solve the problem.&#10;The area of a square with side x is given by the function  &#10;A) 20 square feet&#10;B) 60 square feet&#10;C) 100 square feet&#10;D) 40 square feet

Accepted Answer

The answer of Solve the problem.&#10;The area of a square...

Question 45

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)&#10;

Accepted Answer

The answer of Rewrite the expression without using negative exponents....

Question 46

Find the missing factor or exponent(s).&#10;

Accepted Answer

The answer of Find the missing factor or exponent(s).&#10; ...

Question 47

Find the missing factor or exponent(s).&#10;

Accepted Answer

The answer of Find the missing factor or exponent(s).&#10; ...

Question 48

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)&#10;

Accepted Answer

The answer of Rewrite the expression without using negative exponents....

Question 49

Solve the problem.&#10;The number of feet traveled by a free-falling object in t seconds is given by the function f(t) = 16t How far would it fall in 8 seconds?&#10;A) 64 feet&#10;B) 1024 feet&#10;C) 128 feet&#10;D) 16 feet

Accepted Answer

The answer of Solve the problem.&#10;The number of feet traveled...

Question 50

Evaluate the given function.&#10;

Accepted Answer

The answer of Evaluate the given function.&#10; ...

Question 51

Evaluate the given function.&#10;

Accepted Answer

The answer of Evaluate the given function.&#10; ...

Question 52

Find the missing factor or exponent(s).&#10;

Accepted Answer

The answer of Find the missing factor or exponent(s).&#10; ...

Question 53

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)

--5^ -2

A) 25
B)

- 25

C)

- \frac { 1 } { 25 }

D)

\frac { 1 } { 10 }

Accepted Answer

The answer of Rewrite the expression without using negative exponents....

Question 54

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)&#10;

Accepted Answer

The answer of Rewrite the expression without using negative exponents....

Question 55

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)&#10;

Accepted Answer

The answer of Rewrite the expression without using negative exponents....

Question 56

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 57

Evaluate the given function.&#10;

Accepted Answer

The answer of Evaluate the given function.&#10; ...

Question 58

Find the missing factor or exponent(s).&#10;

Accepted Answer

The answer of Find the missing factor or exponent(s).&#10; ...

Question 59

Find the missing factor or exponent(s).&#10;

Accepted Answer

The answer of Find the missing factor or exponent(s).&#10; ...

Question 60

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)&#10;

Accepted Answer

The answer of Rewrite the expression without using negative exponents....

Question 61

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero&#10;real numbers.)&#10;

Accepted Answer

The answer of Simplify the expression. Write the result without...

Question 62

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero&#10;real numbers.)&#10;

Accepted Answer

The answer of Simplify the expression. Write the result without...

Question 63

Convert the given number to scientific notation.&#10;0.000571

Accepted Answer

The answer of Convert the given number to scientific notation.&#10;0.000571...

Question 64

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero&#10;real numbers.)&#10;

Accepted Answer

The answer of Simplify the expression. Write the result without...

Deck 5: Exponents and Polynomials