Algebra Examples

${(- 16)}^{3} \div {(4^{- 2})}^{- 3}$

Step 1

Rewrite the division as a fraction.

$\frac{{(- 16)}^{3}}{{(4^{- 2})}^{- 3}}$

Step 2

Move ${(4^{- 2})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(- 16)}^{3} {(4^{- 2})}^{3}$

Step 3

Raise $- 16$ to the power of $3$ .

$- 4096 {(4^{- 2})}^{3}$

Step 4

Multiply the exponents in ${(4^{- 2})}^{3}$ .

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Step 4.1

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

$- 4096 \cdot 4^{- 2 \cdot 3}$

Step 4.2

Multiply $- 2$ by $3$ .

$- 4096 \cdot 4^{- 6}$

Step 5

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

$- 4096 \cdot \frac{1}{4^{6}}$

Step 6

Raise $4$ to the power of $6$ .

$- 4096 \cdot \frac{1}{4096}$

Step 7

Cancel the common factor of $4096$ .

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Step 7.1

Factor $4096$ out of $- 4096$ .

$4096 (- 1) \cdot \frac{1}{4096}$

Step 7.2

Cancel the common factor.

$4096 \cdot - 1 \cdot \frac{1}{4096}$

Step 7.3

Rewrite the expression.

$- 1$