Evaluate (25/27)^(3/2)

${(\frac{25}{27})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $\frac{25}{27}$ .

$\frac{25^{\frac{3}{2}}}{27^{\frac{3}{2}}}$

Step 2

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$\frac{{(5^{2})}^{\frac{3}{2}}}{27^{\frac{3}{2}}}$

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

$\frac{5^{2 (\frac{3}{2})}}{27^{\frac{3}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{3}{2})}}{27^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{5^{3}}{27^{\frac{3}{2}}}$

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

$\frac{125}{27^{\frac{3}{2}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{125}{27^{\frac{3}{2}}}$

Decimal Form:

$0.89097263 \dots$