Evaluate ((202^4-122^3-48*2^2)^2)/((-8)^3)

$\frac{{(20 \cdot 2^{4} - 12 \cdot 2^{3} - 48 \cdot 2^{2})}^{2}}{{(- 8)}^{3}}$

Step 1

Simplify the numerator.

Raise $2$ to the power of $4$ .

$\frac{{(20 \cdot 16 - 12 \cdot 2^{3} - 48 \cdot 2^{2})}^{2}}{{(- 8)}^{3}}$

Multiply $20$ by $16$ .

$\frac{{(320 - 12 \cdot 2^{3} - 48 \cdot 2^{2})}^{2}}{{(- 8)}^{3}}$

Raise $2$ to the power of $3$ .

$\frac{{(320 - 12 \cdot 8 - 48 \cdot 2^{2})}^{2}}{{(- 8)}^{3}}$

Multiply $- 12$ by $8$ .

$\frac{{(320 - 96 - 48 \cdot 2^{2})}^{2}}{{(- 8)}^{3}}$

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

$\frac{{(320 - 96 - 48 \cdot 4)}^{2}}{{(- 8)}^{3}}$

Multiply $- 48$ by $4$ .

$\frac{{(320 - 96 - 192)}^{2}}{{(- 8)}^{3}}$

Subtract $96$ from $320$ .

$\frac{{(224 - 192)}^{2}}{{(- 8)}^{3}}$

Subtract $192$ from $224$ .

$\frac{32^{2}}{{(- 8)}^{3}}$

Raise $32$ to the power of $2$ .

$\frac{1024}{{(- 8)}^{3}}$

Step 2

Simplify the expression.

Raise $- 8$ to the power of $3$ .

$\frac{1024}{- 512}$

Divide $1024$ by $- 512$ .

$- 2$

Evaluate ((20*2^4-12*2^3-48*2^2)^2)/((-8)^3)