Simplify ((2^3)^10*2^-8)/(2^-7)

$\frac{{(2^{3})}^{10} \cdot 2^{- 8}}{2^{- 7}}$

Move $2^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(2^{3})}^{10}}{2^{- 7} \cdot 2^{8}}$

Simplify the denominator.

Multiply $2^{- 7}$ by $2^{8}$ by adding the exponents.

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

$\frac{{(2^{3})}^{10}}{2^{- 7 + 8}}$

Add $- 7$ and $8$ .

$\frac{{(2^{3})}^{10}}{2^{1}}$

Simplify $2^{1}$ .

$\frac{{(2^{3})}^{10}}{2}$

Simplify the numerator.

Multiply the exponents in ${(2^{3})}^{10}$ .

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

$\frac{2^{3 \cdot 10}}{2}$

Multiply $3$ by $10$ .

$\frac{2^{30}}{2}$

Raise $2$ to the power of $30$ .

$\frac{1073741824}{2}$

Divide $1073741824$ by $2$ .

$536870912$