Algebra Examples

${(\frac{3^{6}}{12^{6}})}^{- \frac{1}{6}}$

Step 1

Evaluate the exponents.

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Step 1.1

Raise $3$ to the power of $6$ .

${(\frac{729}{12^{6}})}^{- \frac{1}{6}}$

Step 1.2

Raise $12$ to the power of $6$ .

${(\frac{729}{2985984})}^{- \frac{1}{6}}$

Step 2

Cancel the common factor of $729$ and $2985984$ .

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Step 2.1

Factor $729$ out of $729$ .

${(\frac{729 (1)}{2985984})}^{- \frac{1}{6}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $729$ out of $2985984$ .

${(\frac{729 \cdot 1}{729 \cdot 4096})}^{- \frac{1}{6}}$

Step 2.2.2

Cancel the common factor.

${(\frac{729 \cdot 1}{729 \cdot 4096})}^{- \frac{1}{6}}$

Step 2.2.3

Rewrite the expression.

${(\frac{1}{4096})}^{- \frac{1}{6}}$

Step 3

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

$4096^{\frac{1}{6}}$

Step 4

Simplify the expression.

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Step 4.1

Rewrite $4096$ as $4^{6}$ .

${(4^{6})}^{\frac{1}{6}}$

Step 4.2

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

$4^{6 (\frac{1}{6})}$

Step 5

Cancel the common factor of $6$ .

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Step 5.1

Cancel the common factor.

$4^{6 (\frac{1}{6})}$

Step 5.2

Rewrite the expression.

$4^{1}$

Step 6

Evaluate the exponent.

$4$