Algebra Examples

${(\frac{6^{5}}{9^{5}})}^{- \frac{1}{5}}$

Step 1

Raise $6$ to the power of $5$ .

${(\frac{7776}{9^{5}})}^{- \frac{1}{5}}$

Step 2

Raise $9$ to the power of $5$ .

${(\frac{7776}{59049})}^{- \frac{1}{5}}$

Step 3

Cancel the common factor of $7776$ and $59049$ .

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Step 3.1

Factor $243$ out of $7776$ .

${(\frac{243 (32)}{59049})}^{- \frac{1}{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $243$ out of $59049$ .

${(\frac{243 \cdot 32}{243 \cdot 243})}^{- \frac{1}{5}}$

Step 3.2.2

Cancel the common factor.

${(\frac{243 \cdot 32}{243 \cdot 243})}^{- \frac{1}{5}}$

Step 3.2.3

Rewrite the expression.

${(\frac{32}{243})}^{- \frac{1}{5}}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{243}{32})}^{\frac{1}{5}}$

Step 5

Apply the product rule to $\frac{243}{32}$ .

$\frac{243^{\frac{1}{5}}}{32^{\frac{1}{5}}}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite $243$ as $3^{5}$ .

$\frac{{(3^{5})}^{\frac{1}{5}}}{32^{\frac{1}{5}}}$

Step 6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{5 (\frac{1}{5})}}{32^{\frac{1}{5}}}$

Step 6.3

Cancel the common factor of $5$ .

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Step 6.3.1

Cancel the common factor.

$\frac{3^{5 (\frac{1}{5})}}{32^{\frac{1}{5}}}$

Step 6.3.2

Rewrite the expression.

$\frac{3^{1}}{32^{\frac{1}{5}}}$

Step 6.4

Evaluate the exponent.

$\frac{3}{32^{\frac{1}{5}}}$

Step 7

Simplify the denominator.

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Step 7.1

Rewrite $32$ as $2^{5}$ .

$\frac{3}{{(2^{5})}^{\frac{1}{5}}}$

Step 7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3}{2^{5 (\frac{1}{5})}}$

Step 7.3

Cancel the common factor of $5$ .

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Step 7.3.1

Cancel the common factor.

$\frac{3}{2^{5 (\frac{1}{5})}}$

Step 7.3.2

Rewrite the expression.

$\frac{3}{2^{1}}$

Step 7.4

Evaluate the exponent.

$\frac{3}{2}$