Algebra Examples

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

Step 1

Rewrite the division as a fraction.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

Multiply $20$ by $16$ .

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

Step 2.3

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

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

Step 2.4

Multiply $- 12$ by $8$ .

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

Step 2.5

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

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

Step 2.6

Multiply $- 48$ by $4$ .

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

Step 2.7

Subtract $96$ from $320$ .

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

Step 2.8

Subtract $192$ from $224$ .

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

Step 2.9

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

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

Step 3

Simplify the expression.

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Step 3.1

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

$\frac{1024}{- 512}$

Step 3.2

Divide $1024$ by $- 512$ .

$- 2$