Simplify ((2^7)/2)^-4

${(\frac{2^{7}}{2})}^{- 4}$

Step 1

Cancel the common factor of $2^{7}$ and $2$ .

Factor $2$ out of $2^{7}$ .

${(\frac{2 \cdot 2^{6}}{2})}^{- 4}$

Cancel the common factors.

Factor $2$ out of $2$ .

${(\frac{2 \cdot 2^{6}}{2 (1)})}^{- 4}$

Cancel the common factor.

${(\frac{2 \cdot 2^{6}}{2 \cdot 1})}^{- 4}$

Rewrite the expression.

${(\frac{2^{6}}{1})}^{- 4}$

Divide $2^{6}$ by $1$ .

${(2^{6})}^{- 4}$

Step 2

Multiply the exponents in ${(2^{6})}^{- 4}$ .

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

$2^{6 \cdot - 4}$

Multiply $6$ by $- 4$ .

$2^{- 24}$

Step 3

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

$\frac{1}{2^{24}}$

Step 4

Raise $2$ to the power of $24$ .

$\frac{1}{16777216}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{16777216}$

Decimal Form:

$5.96046447 \cdot 10^{- 8}$