Simplifying Exponents - Algebra II

Card 0 of 1232

Question

Simplify.

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

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

Answer

First, combine exponents of like variables. This gives us

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Question

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

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.

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

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 the expression: $\left ( \frac{x^2y^3z^{-2}}{x^{-2}z^4}\right )^{-3}$

Answer

First simplify the expression inside the parentheses.

$\left ( \frac{x^2y^3z^{-2}}{x^{-2}z^4}\right )^{-3}$

$\left ( \frac{x^4y^3}{z^6}\right )^{-3}$

Then distribute the exponent.

$\frac{x^{-12}y^{-9}}{z^{-18}}$

Rearrange the expression so that there are no more negative exponents.

$\frac{z^{18}}{x^{12}y^{9}}$

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Question

Simplify:

Answer

When exponents are being raised by another exponent, we just multiply the powers.

$(10^8)^7=10^{8*7}=10^{56}$

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Question

Simplify:

$(-16^{-5})^{-9}$

Answer

When exponents are being raised by another exponent, we just multiply the powers.

$(-16^{-5})^{-9}=(-16)^{-5*-9}=-16^{45}$

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Question

Simplify:

Answer

When exponents are being raised by another exponent, we just multiply the powers.

$((3^5)^7)^8=3^{578}=3^{280}$

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Question

Simplify.

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

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:

$(24^{12})^{\frac{1}{18}}$

Answer

When exponents are being raised by another exponent, we just multiply the powers.

$(24^{12})^{\frac{1}{18}}=24^{12\frac{1}{18}}=24^{\frac{2}{3}}$

When we have fractional exponents, we convert like this:

$x^{\frac{a}b{}}=\sqrt[b]{x^a}$ . is the index of the radical which is the denominator of the fractional exponent, is the power that will raise the base which is the numerator of the fractional exponent and is the base.

$24^{\frac{2}{3}}=\sqrt[3]{24^2}=\sqrt[3]{576}$ The perfect cube we can get is .

$\sqrt[3]{576}=\sqrt[3]{649}=4\sqrt[3]{9}$

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Question

Simplify:

Answer

To start, we must examine the first term. Note that we are squaring a sum, so we cannot simply distribute the power of 2 to each term. We must take the sum times the sum:

The second term, however, is a product, in which case we can distribute the power:

Adding the two together, we get

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Question

Simplify:

Answer

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

$(2^5)^9=2^{5*9}=2^{45}$

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Question

Simplify: $(17^8)^{-4}$

Answer

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

$(17^8)^{-4}=17^{8*-4}=17^{-32}$

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Question

Simplify: $(3^{-9})^{-9}$

Answer

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

$(3^{-9})^{-9}=3^{-9*-9}=3^{81}$

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Question

Simplify: $(\frac{1}{2}^{9})^8$

Answer

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

$(\frac{1}{2}^{9})^8=\frac{1}{2}^{9*8}=\frac{1}{2}^{72}$

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Question

Simplify:

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

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:

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

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

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:

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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