Simplifying Exponents - Algebra 2

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Question

Simplify: $20^{12}\div20^{-3}$

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Answer

When dividing exponents with the same base, we subtract the exponents while keeping the base the same.

$20^{12}\div20^{-3}=20^{12-(-3)}=20^{15}$

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Question

Simplify:

$9^9\div9^{12}$

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Answer

When exponents with the same base are divided, we will simply subtract the exponents and keep the base the same.

Divide:

$9^9\div9^{12}=9^{9-12}=9^{-3}$

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Question

Simplify: $2^{18}*4^6$

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Answer

Although the bases are not the same, we know that . Therefore, $4^6=(2^2)^6=2^{12}$ . When multiplying exponents with the same base, we just add the exponents and keep the base the same.

$2^{18}*2^{12}=2^{18+12}=2^{30}$

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Question

Simplify: $27^7\div3^9$

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Answer

Although the base is not the same, we know that . Therefore $27^7=(3^3)^7=3^{21}$ . When dividing exponents with the same base, we subtract the exponents while keeping the base the same.

$3^{21}\div3^9=3^{21-9}=3^{12}$

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Question

Simplify:

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Answer

When exponents with the same base are multiplied together, we we will simply add the exponents and keep the base the same.

Multiply:

$8^8*8^8=8^{8+8}=8^{16}$

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Question

Simplify:

$17^5*17^{-6}$

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Answer

When exponents with the same base are multiplied together, we we will simply add the exponents and keep the base the same.

Multiply:

$17^5*17^{-6}=17^{5+(-6)}=17^{-1}$

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Question

Simplify:

$18^{-3}*18^{-4}$

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Answer

When exponents with the same base are multiplied together, we we will simply add the exponents and keep the base the same.

Multiply:

$18^{-3}*18^{-4}=18^{-3+(-4)}=18^{-7}$

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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

Evaluate:

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Answer

When dealing exponents being raised by a power, we multiply the exponents and keep the base.

$(2^9)^4=2^{9*4}=2^{36}$

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Question

Simplify:

$(5^{-8})^{-12}$

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Answer

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

$(5^{-8})^{-12}=5^{-8*-12}=5^{96}$

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