Evaluate (54/64)^(1/3)

${(\frac{54}{64})}^{\frac{1}{3}}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $54$ and $64$ .

Factor $2$ out of $54$ .

${(\frac{2 (27)}{64})}^{\frac{1}{3}}$

Cancel the common factors.

Factor $2$ out of $64$ .

${(\frac{2 \cdot 27}{2 \cdot 32})}^{\frac{1}{3}}$

Cancel the common factor.

${(\frac{2 \cdot 27}{2 \cdot 32})}^{\frac{1}{3}}$

Rewrite the expression.

${(\frac{27}{32})}^{\frac{1}{3}}$

Apply the product rule to $\frac{27}{32}$ .

$\frac{27^{\frac{1}{3}}}{32^{\frac{1}{3}}}$

Step 2

Simplify the numerator.

Rewrite $27$ as $3^{3}$ .

$\frac{{(3^{3})}^{\frac{1}{3}}}{32^{\frac{1}{3}}}$

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

$\frac{3^{3 (\frac{1}{3})}}{32^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3^{3 (\frac{1}{3})}}{32^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{3^{1}}{32^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{3}{32^{\frac{1}{3}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{32^{\frac{1}{3}}}$

Decimal Form:

$0.94494078 \dots$