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Pre-Algebra : Power Rule of Exponents

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Example Questions

Example Question #31 : Power Rule Of Exponents

Simplify the following

(a^4)^2

Possible Answers:

a^8

a^4

a^6

a^2

$a^{42}$

Correct answer:

a^8

Explanation:

When you have the same base and you raise a power to a power, you multiply the exponents. So,

$(a^4)^2 = a^{4 \cdot 2} = a^8$

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Example Question #32 : Power Rule Of Exponents

Simplify the following:

(b^4)^9

Possible Answers:

b^9

$b^{36}$

$b^{49}$

b^5

$b^{13}$

Correct answer:

$b^{36}$

Explanation:

If you are raising a power to another power, you simply multiply the powers together. So,

$(b^4)^9 = b^{4 \cdot 9} = b^{36}$

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Example Question #33 : Power Rule Of Exponents

Simplify the following:

$(a^3)^4 + (b^2)^{-5}$

Possible Answers:

$a^7 + b^{-3}$

$a^{12} + b^{-10}$

$a^7b^{-3}$

$a^{12}b^{-10}$

(ab)^2

Correct answer:

$a^{12} + b^{-10}$

Explanation:

When raising a power to a power, we multiply the exponents. In this case, we get

$(a^3)^4 + (b^2)^{-5}$

$a^{3 \cdot 4} + b^{2 \cdot -5}$

$a^{12} + b^{-10}$

And since they have different bases, we cannot combine them any further.

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Example Question #34 : Power Rule Of Exponents

Which answer shows the answer to:

19^8 * 19^4 =

Possible Answers:

19^4

19^2

19^3^2

19^1^2

19^1^6

Correct answer:

19^1^2

Explanation:

19 is the base number. It is the same on both sides.

If the base is the same on both sides and it is a multiplication problem we keep the base and add the exponents together.

19^8 ^ + ^4

= 19^1^2

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Example Question #35 : Power Rule Of Exponents

Simplify the following:

$(x^2)^{-3} + (y^{-3})^4$

Possible Answers:

$x^{-6}y^{-12}$

$x^{-1} + y^{-7}$

$x^{-6} + y^{-12}$

$x^{-5}y$

$x^{-5} + y$

Correct answer:

$x^{-6} + y^{-12}$

Explanation:

The power rule for exponents states that when you raise a power to a power, you multiply the exponents, keeping the base the same. So,

$(x^2)^{-3} + (y^{-3})^4$

can be written as

$x^{\ 2 \ \cdot \ -3} + y^{\ -3 \ \cdot \ 4}$

$x^{-6} + y^{-12}$

Since we cannot combine two different bases, this is now in simplest form.

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Example Question #36 : Power Rule Of Exponents

Simplify the polynomial.

$(2m^{2}n^{4}y^{3})^{2}$

Possible Answers:

$4m^{4}n^{8}y^{6}$

$4mny^{18}$

$4m^{2}n^{4}y^{3}$

$4m^{4}n^{6}y^{5}$

$4mny^{8}$

Correct answer:

$4m^{4}n^{8}y^{6}$

Explanation:

In order to solve this problem you must take every integer and variable to the power of 2 like so,

$(2m^{2}n^{4}y^{3})^{2}= 2^{2}m^{2\cdot 2}n^{4\cdot 2}y^{3\cdot 2}=4m^{4}n^{8}y^{6}$

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Example Question #37 : Power Rule Of Exponents

Simplify the following:

$({x^{9}})^6$ +(y^3)^4

Possible Answers:

$x^{{15}}+y^{12}$

$x^{{54}}+y^{7}$

$x^{{54}}+y^{12}$

$x^{{15}}+y^{7}$

None of the above

Correct answer:

$x^{{54}}+y^{12}$

Explanation:

When you raise an exponent to an additional power you need to multiply the two numbers, so you will get:

$x^{{9*6}}+y^{3*4}$ which equals $x^{{54}}+y^{12}$

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Pre-Algebra : Power Rule of Exponents

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #31 : Power Rule Of Exponents

Example Question #32 : Power Rule Of Exponents

Example Question #33 : Power Rule Of Exponents

Example Question #34 : Power Rule Of Exponents

Example Question #35 : Power Rule Of Exponents

Example Question #36 : Power Rule Of Exponents

Example Question #37 : Power Rule Of Exponents

All Pre-Algebra Resources

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