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High School Math : How to use the power rule for exponents in pre-algebra

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Example Question #1 : How To Use The Power Rule For Exponents In Pre Algebra

Simplify the exponential expression below.

$(2^{4})^{6}$

Possible Answers:

$2^{10}$

$12^{4}$

$2^{24}$

$2^{2}$

Correct answer:

$2^{24}$

Explanation:

The power rule of exponents states that when an exponential term is raised to another power, we multiply the exponents to simplify.

$(2^{4})^{6}=2^{4*6}=2^{24}$

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Example Question #2 : How To Use The Power Rule For Exponents In Pre Algebra

What is the value of (X^2)^4 ?

Possible Answers:

X^8

X^6

X^2

X^5

Correct answer:

X^8

Explanation:

The power rule says that an exponent to the power of another exponent gets multiplied. We can think of (X^2)^4 as $X^2 \times X^2 \times X^2 \times X^2$ , in which case we see that the answer is X^8 because multiplying the same numbers with different exponents adds the exponents.

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Example Question #3 : How To Use The Power Rule For Exponents In Pre Algebra

Simplify $(x^{4})^{3}$ .

Possible Answers:

x^4

$x^{12}$

$x^{7}$

x^3

Correct answer:

$x^{12}$

Explanation:

When raising a polynomial to a power you multiply the polynomial inside the parentheses by the power outside of the parentheses.

If you think about it $(x^{4})^{3}$ is equivalent to (x*x*x*x)(x*x*x*x)(x*x*x*x)

So we multiply by to get the power of the answer

The answer is $x^{12}$ .

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Example Question #2 : How To Use The Power Rule For Exponents In Pre Algebra

Simplify the expression.

(y^4)^5

Possible Answers:

5y^4

y^9

y^2^0

y^1

20y

Correct answer:

y^2^0

Explanation:

The power rule of exponents states than an exponential term raised to another exponent can be simplified by multiplying the exponents together.

(y^4)^5

$(y)^{4*5}$

$y^{20}$

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Example Question #5 : How To Use The Power Rule For Exponents In Pre Algebra

What is $(x^{6})^{8}$ simplified?

Possible Answers:

$x^{\frac{6}{8}}$

$x^{48}$

$x^{2}$

$x^{14}$

Correct answer:

$x^{48}$

Explanation:

When raising a polynomial to a power you multiply the polynomial inside the parentheses by the power outside of the parentheses.

So we multiply by to get the power of the answer as .

The answer is $x^{48}$ .

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Example Question #6 : How To Use The Power Rule For Exponents In Pre Algebra

What is $(x^{5})^{9}$ simplified?

Possible Answers:

$x^{29}$

$x^{45}$

$x^{14}$

$x^{4}$

Correct answer:

$x^{45}$

Explanation:

When raising a polynomial to a power, you multiply the exponent inside the parentheses by the power outside of the parentheses.

So we multiply by to get the power of the answer, which is .

The answer is $x^{45}$ .

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Example Question #2 : How To Use The Power Rule For Exponents In Pre Algebra

What is the value of 9^₃?

Possible Answers:

19,683

490

729

Correct answer:

729

Explanation:

Exponents are a way of expressing the repeated multiplication of the same value. An exponent describes how many times a value is to be multiplied by itself.

$9^{3}=9\cdot 9\cdot 9=729$

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Example Question #3 : How To Use The Power Rule For Exponents In Pre Algebra

Which of the following is an alternate positive expression of 4^-3?

Possible Answers:

$4^{3}$

$1/4^{-3}$

$3^{4}$

$4^{3}/1$

$1/4^{3}$

Correct answer:

$1/4^{3}$

Explanation:

You can simplify negative exponents in order to work only with positive numbers. Simply make the negative number positive and divide 1 by the entire expression.

$4^{-3}=1/4^{3}$

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Example Question #9 : How To Use The Power Rule For Exponents In Pre Algebra

Simplify $(x^{5})^{12}$

Possible Answers:

$x^{-7}$

$x^{60}$

$x^{17}$

$x^{7}$

Correct answer:

$x^{60}$

Explanation:

When raising an exponent to another exponent you multiply the exponent inside the parentheses by the exponent outside of the parentheses.

So we multiply by to get the final exponent, which is .

The answer is $x^{60}$ .

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Example Question #4 : How To Use The Power Rule For Exponents In Pre Algebra

Simplify $(x^{5})^{4}$ .

Possible Answers:

$x^{20}$

$x^{9}$

$4x^{5}$

Correct answer:

$x^{20}$

Explanation:

When raising a polynomial to a power, multiply the polynomial inside the parentheses by the power outside of the parentheses.

We multiply by to get the power of the answer, .

The answer is $x^{20}$ .

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High School Math : How to use the power rule for exponents in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #2 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #3 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #2 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #5 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #6 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #2 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #3 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #9 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #4 : How To Use The Power Rule For Exponents In Pre Algebra

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