Simplify (512/216)^(1/3)

${(\frac{512}{216})}^{\frac{1}{3}}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $512$ and $216$ .

Factor $8$ out of $512$ .

${(\frac{8 (64)}{216})}^{\frac{1}{3}}$

Cancel the common factors.

Factor $8$ out of $216$ .

${(\frac{8 \cdot 64}{8 \cdot 27})}^{\frac{1}{3}}$

Cancel the common factor.

${(\frac{8 \cdot 64}{8 \cdot 27})}^{\frac{1}{3}}$

Rewrite the expression.

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

Apply the product rule to $\frac{64}{27}$ .

$\frac{64^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

Step 2

Simplify the numerator.

Rewrite $64$ as $4^{3}$ .

$\frac{{(4^{3})}^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

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

$\frac{4^{3 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4^{3 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{4^{1}}{27^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{4}{27^{\frac{1}{3}}}$

Step 3

Simplify the denominator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$

Simplify (512/216)^(1/3)

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