Evaluate (216/343)^(2/3)

${(\frac{216}{343})}^{\frac{2}{3}}$

Step 1

Apply the product rule to $\frac{216}{343}$ .

$\frac{216^{\frac{2}{3}}}{343^{\frac{2}{3}}}$

Step 2

Simplify the numerator.

Rewrite $216$ as $6^{3}$ .

$\frac{{(6^{3})}^{\frac{2}{3}}}{343^{\frac{2}{3}}}$

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

$\frac{6^{3 (\frac{2}{3})}}{343^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{6^{3 (\frac{2}{3})}}{343^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{6^{2}}{343^{\frac{2}{3}}}$

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

$\frac{36}{343^{\frac{2}{3}}}$

Step 3

Simplify the denominator.

Rewrite $343$ as $7^{3}$ .

$\frac{36}{{(7^{3})}^{\frac{2}{3}}}$

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

$\frac{36}{7^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{36}{7^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{36}{7^{2}}$

Raise $7$ to the power of $2$ .

$\frac{36}{49}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{36}{49}$

Decimal Form:

$0.73469387 \dots$