Evaluate ((-16)^3)÷((4^-2)^-3)

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

Rewrite the division as a fraction.

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

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

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

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

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

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

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

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

Multiply $- 2$ by $3$ .

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

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

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

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

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

Cancel the common factor of $4096$ .

Factor $4096$ out of $- 4096$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 1$