Simplify ((4^5)(4^-2))/(4^-7)

$\frac{(4^{5}) (4^{- 2})}{4^{- 7}}$

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

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

$\frac{4^{5 - 2}}{4^{- 7}}$

Subtract $2$ from $5$ .

$\frac{4^{3}}{4^{- 7}}$

Move $4^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4^{3} \cdot 4^{7}$

Multiply $4^{3}$ by $4^{7}$ by adding the exponents.

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

$4^{3 + 7}$

Add $3$ and $7$ .

$4^{10}$

Raise $4$ to the power of $10$ .

$1048576$