Evaluate ((8^2)/(4^4))^3

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

Evaluate the exponents.

Raise $8$ to the power of $2$ .

${(\frac{64}{4^{4}})}^{3}$

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

${(\frac{64}{256})}^{3}$

${(\frac{64}{256})}^{3}$

Cancel the common factor of $64$ and $256$ .

Factor $64$ out of $64$ .

${(\frac{64 (1)}{256})}^{3}$

Cancel the common factors.

Factor $64$ out of $256$ .

${(\frac{64 \cdot 1}{64 \cdot 4})}^{3}$

Cancel the common factor.

${(\frac{64 \cdot 1}{64 \cdot 4})}^{3}$

Rewrite the expression.

${(\frac{1}{4})}^{3}$

${(\frac{1}{4})}^{3}$

${(\frac{1}{4})}^{3}$

Simplify the expression.

Apply the product rule to $\frac{1}{4}$ .

$\frac{1^{3}}{4^{3}}$

One to any power is one.

$\frac{1}{4^{3}}$

Raise $4$ to the power of $3$ .

$\frac{1}{64}$

$\frac{1}{64}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{64}$

Decimal Form:

$0.015625$

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