Calculus Examples

${(\frac{1}{16})}^{- \frac{1}{4}} {(\frac{27}{64})}^{- \frac{1}{3}}$

Step 1

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

$16^{\frac{1}{4}} {(\frac{27}{64})}^{- \frac{1}{3}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $16$ as $2^{4}$ .

${(2^{4})}^{\frac{1}{4}} {(\frac{27}{64})}^{- \frac{1}{3}}$

Step 2.2

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

$2^{4 (\frac{1}{4})} {(\frac{27}{64})}^{- \frac{1}{3}}$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

$2^{4 (\frac{1}{4})} {(\frac{27}{64})}^{- \frac{1}{3}}$

Step 3.2

Rewrite the expression.

$2^{1} {(\frac{27}{64})}^{- \frac{1}{3}}$

Step 4

Evaluate the exponent.

$2 {(\frac{27}{64})}^{- \frac{1}{3}}$

Step 5

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

$2 {(\frac{64}{27})}^{\frac{1}{3}}$

Step 6

Apply the product rule to $\frac{64}{27}$ .

$2 \frac{64^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

Step 7

Simplify the numerator.

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Step 7.1

Rewrite $64$ as $4^{3}$ .

$2 \frac{{(4^{3})}^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

Step 7.2

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

$2 \frac{4^{3 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Step 7.3

Cancel the common factor of $3$ .

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Step 7.3.1

Cancel the common factor.

$2 \frac{4^{3 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Step 7.3.2

Rewrite the expression.

$2 \frac{4^{1}}{27^{\frac{1}{3}}}$

Step 7.4

Evaluate the exponent.

$2 \frac{4}{27^{\frac{1}{3}}}$

Step 8

Simplify the denominator.

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Step 8.1

Rewrite $27$ as $3^{3}$ .

$2 \frac{4}{{(3^{3})}^{\frac{1}{3}}}$

Step 8.2

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

$2 \frac{4}{3^{3 (\frac{1}{3})}}$

Step 8.3

Cancel the common factor of $3$ .

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Step 8.3.1

Cancel the common factor.

$2 \frac{4}{3^{3 (\frac{1}{3})}}$

Step 8.3.2

Rewrite the expression.

$2 \frac{4}{3^{1}}$

Step 8.4

Evaluate the exponent.

$2 (\frac{4}{3})$

Step 9

Multiply $2 (\frac{4}{3})$ .

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Step 9.1

Combine $2$ and $\frac{4}{3}$ .

$\frac{2 \cdot 4}{3}$

Step 9.2

Multiply $2$ by $4$ .

$\frac{8}{3}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{3}$

Decimal Form:

$2.\overline{6}$

Mixed Number Form:

$2 \frac{2}{3}$