Algebra Examples

$M = {(- \frac{1}{8})}^{- 3^{- 1}} + {(\frac{1}{16})}^{- 4^{- 1}}$

Step 1

Simplify each term.

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Step 1.1

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

$M = {(- \frac{1}{8})}^{- \frac{1}{3}} + {(\frac{1}{16})}^{- 4^{- 1}}$

Step 1.2

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

$M = {(- 8)}^{\frac{1}{3}} + {(\frac{1}{16})}^{- 4^{- 1}}$

Step 1.3

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$M = {({(- 2)}^{3})}^{\frac{1}{3}} + {(\frac{1}{16})}^{- 4^{- 1}}$

Step 1.4

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

$M = {(- 2)}^{3 (\frac{1}{3})} + {(\frac{1}{16})}^{- 4^{- 1}}$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Cancel the common factor.

$M = {(- 2)}^{3 (\frac{1}{3})} + {(\frac{1}{16})}^{- 4^{- 1}}$

Step 1.5.2

Rewrite the expression.

$M = {(- 2)}^{1} + {(\frac{1}{16})}^{- 4^{- 1}}$

Step 1.6

Evaluate the exponent.

$M = - 2 + {(\frac{1}{16})}^{- 4^{- 1}}$

Step 1.7

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

$M = - 2 + {(\frac{1}{16})}^{- \frac{1}{4}}$

Step 1.8

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

$M = - 2 + 16^{\frac{1}{4}}$

Step 1.9

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

$M = - 2 + {(2^{4})}^{\frac{1}{4}}$

Step 1.10

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

$M = - 2 + 2^{4 (\frac{1}{4})}$

Step 1.11

Cancel the common factor of $4$ .

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Step 1.11.1

Cancel the common factor.

$M = - 2 + 2^{4 (\frac{1}{4})}$

Step 1.11.2

Rewrite the expression.

$M = - 2 + 2^{1}$

Step 1.12

Evaluate the exponent.

$M = - 2 + 2$

Step 2

Add $- 2$ and $2$ .

$M = 0$