Simplify (2^5*8^2)/(16^-3)

$\frac{2^{5} \cdot 8^{2}}{16^{- 3}}$

Step 1

Move $16^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2^{5} \cdot 8^{2} \cdot 16^{3}$

Step 2

Rewrite $8$ as $2^{3}$ .

$2^{5} \cdot {(2^{3})}^{2} \cdot 16^{3}$

Step 3

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

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

$2^{5} \cdot 2^{3 \cdot 2} \cdot 16^{3}$

Multiply $3$ by $2$ .

$2^{5} \cdot 2^{6} \cdot 16^{3}$

Step 4

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

$2^{5 + 6} \cdot 16^{3}$

Step 5

Add $5$ and $6$ .

$2^{11} \cdot 16^{3}$

Step 6

Raise $2$ to the power of $11$ .

$2048 \cdot 16^{3}$

Step 7

Raise $16$ to the power of $3$ .

$2048 \cdot 4096$

Step 8

Multiply $2048$ by $4096$ .

$8388608$