Evaluate ((-2^2)^38)/(4^4(0.5)^3)

$\frac{{(- 2^{2})}^{3} \cdot 8}{4^{4} \cdot {(0.5)}^{3}}$

Step 1

Simplify the numerator.

Apply the product rule to $- 2^{2}$ .

$\frac{{(- 1)}^{3} {(2^{2})}^{3} \cdot 8}{4^{4} \cdot {0.5}^{3}}$

Raise $- 1$ to the power of $3$ .

$\frac{- {(2^{2})}^{3} \cdot 8}{4^{4} \cdot {0.5}^{3}}$

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

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

$\frac{- 2^{2 \cdot 3} \cdot 8}{4^{4} \cdot {0.5}^{3}}$

Multiply $2$ by $3$ .

$\frac{- 2^{6} \cdot 8}{4^{4} \cdot {0.5}^{3}}$

Raise $2$ to the power of $6$ .

$\frac{- 1 \cdot 64 \cdot 8}{4^{4} \cdot {0.5}^{3}}$

Combine exponents.

Multiply $- 1$ by $64$ .

$\frac{- 64 \cdot 8}{4^{4} \cdot {0.5}^{3}}$

Multiply $- 64$ by $8$ .

$\frac{- 512}{4^{4} \cdot {0.5}^{3}}$

Step 2

Simplify the denominator.

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

$\frac{- 512}{256 \cdot {0.5}^{3}}$

Raise $0.5$ to the power of $3$ .

$\frac{- 512}{256 \cdot 0.125}$

Step 3

Simplify the expression.

Multiply $256$ by $0.125$ .

$\frac{- 512}{32}$

Divide $- 512$ by $32$ .

$- 16$

Evaluate ((-2^2)^3*8)/(4^4*(0.5)^3)