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Algebra II : Simple Exponents

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Example Questions

Example Question #31 : Simple Exponents

Expand:

12^4

Possible Answers:

12*12*12*12*4*4*4*4

144*16

4*4*4*4*4*4*4*4*4*4*4*4

12*4

12*12*12*12

Correct answer:

12*12*12*12

Explanation:

When expanding exponents, we simply multiply the base by itself for the number of times indicated by the exponential value.

12^4=12*12*12*12

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Example Question #32 : Simple Exponents

Evaluate:

7^4

Possible Answers:

4703

2603

7777

2401

4949

Correct answer:

2401

Explanation:

When expanding exponents, we simply multiply the base by itself for the number of times indicated by the exponential value.

7^4 is expanded out to 7*7*7*7 .

When we multiply the numbers, we get a product of 2401 .

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Example Question #32 : Simple Exponents

Convert to base .

Possible Answers:

2^2

2^4

2^8

2^6

2^3

Correct answer:

2^4

Explanation:

First, we know that is divisible by .

Therefore:

16=2^4

The answer is:

2^4

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Example Question #33 : Simple Exponents

Convert $2^{15}$ to base .

Possible Answers:

8^9

8^6

8^4

$8^{12}$

8^5

Correct answer:

8^5

Explanation:

First, we know is divisible by .

Therefore:

8=2^3

We can set-up an equation by applying the power rule of exponents.

$2^{15}=(2^3)^x$

When a number to a power is raised by an exponent, we add the exponents. Write an equation and solve for .

3x=15

Simplify.

x=5

The answer is:

8^5

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Example Question #34 : Simple Exponents

Convert $3^{72}$ to base .

Possible Answers:

$9^{24}$

$9^{70}$

$9^{36}$

$9^{48}$

$9^{12}$

Correct answer:

$9^{36}$

Explanation:

First, know is divisible by .

Therefore:

9=3^2

We can set-up an equation by applying the power rule of exponents.

$3^{72}=(3^2)^x$

When a number to a power is raised by an exponent, we add the exponents. Write an equation and solve for .

2x=72

Simplify.

x=36

The answer is:

$9^{36}$

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Example Question #35 : Simple Exponents

Convert 27^4 to base

Possible Answers:

$3^{9}$

$3^{12}$

$3^{15}$

$3^{18}$

$3^{7}$

Correct answer:

$3^{12}$

Explanation:

First, we know the following:

27=3^3

In order to figure out the whole exponent, we can apply the power rule for exponents.

$27^4=(3^3)^4=3^{12}$

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Example Question #36 : Simple Exponents

Evaluate:

$\frac{1}{5}^2$

Possible Answers:

$\frac{2}{5}$

$\frac{1}{25}$

$\frac{2}{25}$

$\frac{1}{10}$

Correct answer:

$\frac{1}{25}$

Explanation:

We can expand $\frac{1}{5}^2$ to the following:

$\frac{1}{5}*\frac{1}{5}$

The product is:

$\frac{1}{25}$

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Example Question #37 : Simple Exponents

Evaluate:

$\frac{3}{4}^3$

Possible Answers:

$\frac{9}{16}$

$\frac{27}{12}$

$\frac{9}{64}$

$\frac{27}{34}$

$\frac{27}{64}$

Correct answer:

$\frac{27}{64}$

Explanation:

We can expand $\frac{3}{4}^3$ to the following:

$\frac{3}{4}*\frac{3}{4}*\frac{3}{4}$

The product is:

$\frac{27}{64}$

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Example Question #38 : Simple Exponents

Convert $\frac{1}{32}$ to base $\frac{1}{2}$

Possible Answers:

$\frac{1}{2}^7$

$\frac{1}{2}^{18}$

$\frac{1}{2}^{16}$

$\frac{1}{2}^5$

$\frac{1}{2}^4$

Correct answer:

$\frac{1}{2}^5$

Explanation:

First, we know that $\frac{1}{32}$ is divisible by $\frac{1}{2}$ .

The conversion becomes:

$\frac{1}{2}^5$

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Example Question #39 : Simple Exponents

Convert $\frac{1}{125}$ to base $\frac{1}{5}$ .

Possible Answers:

$\frac{1}{5}^3$

$\frac{1}{5}^{25}$

$\frac{1}{5}^{10}$

$\frac{1}{5}^4$

$\frac{1}{5}^2$

Correct answer:

$\frac{1}{5}^3$

Explanation:

First, we know that $\frac{1}{125}$ is divisible by $\frac{1}{5}$ .

The conversion becomes:

$\frac{1}{5}^3$

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Algebra II : Simple Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #31 : Simple Exponents

Example Question #32 : Simple Exponents

Example Question #32 : Simple Exponents

Example Question #33 : Simple Exponents

Example Question #34 : Simple Exponents

Example Question #35 : Simple Exponents

Example Question #36 : Simple Exponents

Example Question #37 : Simple Exponents

Example Question #38 : Simple Exponents

Example Question #39 : Simple Exponents

All Algebra II Resources

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