Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $3$ .

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

Step 1.4

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

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

Step 1.5

Combine exponents.

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Step 1.5.1

Multiply $- 1$ by $64$ .

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

Step 1.5.2

Multiply $- 64$ by $8$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify the expression.

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Step 3.1

Multiply $256$ by $0.125$ .

$\frac{- 512}{32}$

Step 3.2

Divide $- 512$ by $32$ .

$- 16$