Simplifying Exponents - Algebra 2

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Question

Simplify:

$\left(\frac{1}{3}^7\right)^{-7}$

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Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$\left(\frac{1}{3}^7\right)^{-7}=\frac{1}{3}^{7*-7}=\frac{1}{3}^{-49}$

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Question

Simplify:

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Answer

When dealing with exponents raising another exponent, we just multiply the powers and keep the base the same.

$(8^8)^8=8^{8*8}=8^{64}$

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Question

Simplify: $(9^9)^{-9}$

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Answer

When dealing with exponents raising another exponent, we just multiply the powers and keep the base the same.

$(9^9)^{-9}=9^{-9*9}=9^{-81}$

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Question

Simplify: $(11^{-11})^{-11}$

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Answer

When dealing with exponents raising another exponent, we just multiply the powers and keep the base the same.

$(11^{-11})^{-11}=11^{-11*-11}=11^{121}$

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Question

Simplify:

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Answer

Although we don't have the same base, we know that . Therefore

When multiplying exponents with the same base, we just add the exponents and keep the base the same.

$6^7*6^6=6^{6+7}=6^{13}$

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Question

Simplify: $144^6\div12^7$

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Answer

Although we don't have the same base, we know that . Therefore we have $144^6\div12^7=(12^2)^6\div12^7=12^{12}\div12^7$

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

$12^{12}\div12^7=12^{12-7}=12^5$

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Question

Simplify: $(19^\frac{2}{3})^9$

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Answer

When dealing with exponents raising another exponent, we just multiply the powers and keep the base the same.

$(19^\frac{2}{3})^9=19^{\frac{2}{3}*9}=19^6$

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Question

Simplify $(x^{-6}x^{4})^{3}$ .

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Answer

The problem uses both the Power of a Product Property and the Power of a Power Property of exponents.

$x^{a}x^{b}=x^{a+b}$

$(x^{a})^{b}=x^{ab}$

First multiply the terms inside the parentheses:

$(x^{-6}x^{4})^{3}=(x^{-6+4})^{3}=(x^{-2})^{3}$

Now raise the term to the 3rd power:

$(x^{-2})^{3}=x^{-2\cdot 3}=x^{-6}$

Negative exponents mean that the term belongs in the denominator:

$x^{-6}=\frac{1}{x^{6}}$

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Question

Simplify $x^5y^2x^{-4}$

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Answer

First, combine exponents of like variables. This gives us

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Question

Simplify $z^3y^2x^6y^{-3}$

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Answer

First, combine exponents of like variables. This gives us $z^3y^{-1}x^6$ which simplifies to $\frac{z^3x^6}{y}$

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Question

Simplify.

$3^{-14}3^{23}3^{-15}$

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Answer

When multiplying exponents with the same base, you just have to add the exponents.

$3^{-14}3^{23}3^{-15}=3^{-14+23-15}=3^{-6}$

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Question

Simplify.

$\frac{a^{45}}{a^{30}}$

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Answer

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{45}}{a^{30}}=a^{45-30}=a^{15}$

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Question

Simplify.

$\frac{a^7}{a^{18}}$

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Answer

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{7}}{a^{18}}=a^{7-18}=a^{-11}$

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Question

Simplify: $12^{19}\div12^7$

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Answer

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

$12^{19}\div12^7=12^{19-7}=12^{12}$

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Question

Simplify:

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Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$23^7*23^8=23^{7+8}=23^{15}$

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Question

Simplify: $2^4*2^{-12}$

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Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$2^4*2^{-12}=2^{4+(-12)}=2^{-8}$

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Question

Simplify: $(-3)^7*(-3)^{-2}$

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Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$(-3)^7*(-3)^{-2}=(-3)^{7+(-2)}=(-3)^{5}$

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Question

Simplify:

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Answer

When multiplying exponents with the same base, we just keep the base the same and add the exponents.

$x^5*x^6=x^{5+6}=x^{11}$

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Question

Simplify: $x^{12}*x^{-8}$

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Answer

When multiplying exponents with the same base, we just keep the base the same and add the exponents.

$x^{12}*x^{-8}=x^{12+(-8)}=x^4$

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Question

Simplify:

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

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Answer

The power that's outside of the parentheses needs to be distributed to every term inside the parentheses:

$-2^3x^{-2\cdot 3}y^{3\cdot 3}$ .

When there's a power outside the parentheses, the exponents are multiplied:

$-8x^{-6}y^9$ .

To get rid of the negative exponent, put it on the denominator:

$\frac{-8y^9}{x^6}$ .

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