Convert to a Simplified Fraction ((4^3)/(5^-2))^5

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

Step 1

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

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

Step 2

Raise $4$ to the power of $3$ .

${(64 \cdot 5^{2})}^{5}$

Step 3

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

${(64 \cdot 25)}^{5}$

Step 4

Multiply $64$ by $25$ .

$1600^{5}$

Step 5

Raise $1600$ to the power of $5$ .

$10485760000000000$