Simplify (2^3)^4*(2^3)^-5

${(2^{3})}^{4} \cdot {(2^{3})}^{- 5}$

Multiply ${(2^{3})}^{4}$ by ${(2^{3})}^{- 5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(2^{3})}^{4 - 5}$

Subtract $5$ from $4$ .

${(2^{3})}^{- 1}$

Multiply the exponents in ${(2^{3})}^{- 1}$ .

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

$2^{3 \cdot - 1}$

Multiply $3$ by $- 1$ .

$2^{- 3}$

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

$\frac{1}{2^{3}}$

Raise $2$ to the power of $3$ .

$\frac{1}{8}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$