Simplify ((3^6)/(5^3))^(2/3)

${(\frac{3^{6}}{5^{3}})}^{\frac{2}{3}}$

Step 1

Simplify the expression.

Raise $3$ to the power of $6$ .

${(\frac{729}{5^{3}})}^{\frac{2}{3}}$

Raise $5$ to the power of $3$ .

${(\frac{729}{125})}^{\frac{2}{3}}$

Apply the product rule to $\frac{729}{125}$ .

$\frac{729^{\frac{2}{3}}}{125^{\frac{2}{3}}}$

Step 2

Simplify the numerator.

Rewrite $729$ as $9^{3}$ .

$\frac{{(9^{3})}^{\frac{2}{3}}}{125^{\frac{2}{3}}}$

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

$\frac{9^{3 (\frac{2}{3})}}{125^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{9^{3 (\frac{2}{3})}}{125^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{9^{2}}{125^{\frac{2}{3}}}$

Raise $9$ to the power of $2$ .

$\frac{81}{125^{\frac{2}{3}}}$

Step 3

Simplify the denominator.

Rewrite $125$ as $5^{3}$ .

$\frac{81}{{(5^{3})}^{\frac{2}{3}}}$

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

$\frac{81}{5^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{81}{5^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{81}{5^{2}}$

Raise $5$ to the power of $2$ .

$\frac{81}{25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{25}$

Decimal Form:

$3.24$

Mixed Number Form:

$3 \frac{6}{25}$