Basic Math Examples

${(4^{- 4} \cdot 8^{8})}^{- \frac{1}{4}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{4^{4}} \cdot 8^{8})}^{- \frac{1}{4}}$

Step 2

Evaluate the exponents.

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Step 2.1

Raise $4$ to the power of $4$ .

${(\frac{1}{256} \cdot 8^{8})}^{- \frac{1}{4}}$

Step 2.2

Raise $8$ to the power of $8$ .

${(\frac{1}{256} \cdot 16777216)}^{- \frac{1}{4}}$

Step 3

Cancel the common factor of $256$ .

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Step 3.1

Factor $256$ out of $16777216$ .

${(\frac{1}{256} \cdot (256 (65536)))}^{- \frac{1}{4}}$

Step 3.2

Cancel the common factor.

${(\frac{1}{256} \cdot (256 \cdot 65536))}^{- \frac{1}{4}}$

Step 3.3

Rewrite the expression.

$65536^{- \frac{1}{4}}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{65536^{\frac{1}{4}}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $65536$ as $16^{4}$ .

$\frac{1}{{(16^{4})}^{\frac{1}{4}}}$

Step 5.2

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

$\frac{1}{16^{4 (\frac{1}{4})}}$

Step 5.3

Cancel the common factor of $4$ .

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Step 5.3.1

Cancel the common factor.

$\frac{1}{16^{4 (\frac{1}{4})}}$

Step 5.3.2

Rewrite the expression.

$\frac{1}{16^{1}}$

Step 5.4

Evaluate the exponent.

$\frac{1}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{16}$

Decimal Form:

$0.0625$