Calculus Examples

${(\frac{1}{16})}^{- \frac{1}{4}} {(\frac{27}{216})}^{- \frac{1}{3}}$

Step 1

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

$16^{\frac{1}{4}} {(\frac{27}{216})}^{- \frac{1}{3}}$

Step 2

Simplify the expression.

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Step 2.1

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

${(2^{4})}^{\frac{1}{4}} {(\frac{27}{216})}^{- \frac{1}{3}}$

Step 2.2

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

$2^{4 (\frac{1}{4})} {(\frac{27}{216})}^{- \frac{1}{3}}$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

$2^{4 (\frac{1}{4})} {(\frac{27}{216})}^{- \frac{1}{3}}$

Step 3.2

Rewrite the expression.

$2^{1} {(\frac{27}{216})}^{- \frac{1}{3}}$

Step 4

Evaluate the exponent.

$2 {(\frac{27}{216})}^{- \frac{1}{3}}$

Step 5

Cancel the common factor of $27$ and $216$ .

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Step 5.1

Factor $27$ out of $27$ .

$2 {(\frac{27 (1)}{216})}^{- \frac{1}{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $27$ out of $216$ .

$2 {(\frac{27 \cdot 1}{27 \cdot 8})}^{- \frac{1}{3}}$

Step 5.2.2

Cancel the common factor.

$2 {(\frac{27 \cdot 1}{27 \cdot 8})}^{- \frac{1}{3}}$

Step 5.2.3

Rewrite the expression.

$2 {(\frac{1}{8})}^{- \frac{1}{3}}$

Step 6

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

$2 \cdot 8^{\frac{1}{3}}$

Step 7

Simplify the expression.

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Step 7.1

Rewrite $8$ as $2^{3}$ .

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

Step 7.2

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

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

Step 8

Cancel the common factor of $3$ .

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Step 8.1

Cancel the common factor.

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

Step 8.2

Rewrite the expression.

$2 \cdot 2^{1}$

Step 9

Evaluate the exponent.

$2 \cdot 2$

Step 10

Multiply $2$ by $2$ .

$4$