Simplify ((2^-1)^-5)/(2^4)

$\frac{{(2^{- 1})}^{- 5}}{2^{4}}$

Step 1

Move ${(2^{- 1})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2^{4} {(2^{- 1})}^{5}}$

Step 2

Simplify the denominator.

Raise $2$ to the power of $4$ .

$\frac{1}{16 {(2^{- 1})}^{5}}$

Multiply the exponents in ${(2^{- 1})}^{5}$ .

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

$\frac{1}{16 \cdot 2^{- 1 \cdot 5}}$

Multiply $- 1$ by $5$ .

$\frac{1}{16 \cdot 2^{- 5}}$

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

$\frac{1}{16 \frac{1}{2^{5}}}$

Raise $2$ to the power of $5$ .

$\frac{1}{16 (\frac{1}{32})}$

Step 3

Simplify terms.

Combine $16$ and $\frac{1}{32}$ .

$\frac{1}{\frac{16}{32}}$

Cancel the common factor of $16$ and $32$ .

Factor $16$ out of $16$ .

$\frac{1}{\frac{16 (1)}{32}}$

Cancel the common factors.

Factor $16$ out of $32$ .

$\frac{1}{\frac{16 \cdot 1}{16 \cdot 2}}$

Cancel the common factor.

$\frac{1}{\frac{16 \cdot 1}{16 \cdot 2}}$

Rewrite the expression.

$\frac{1}{\frac{1}{2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$1 \cdot 2$

Step 5

Multiply $2$ by $1$ .

$2$