Convert to Radical Form ((125^2)/(125^(4/3)))

$(\frac{125^{2}}{125^{\frac{4}{3}}})$

Step 1

Move $125^{\frac{4}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$(125^{2} \cdot 125^{- \frac{4}{3}})$

Step 2

Multiply $125^{2}$ by $125^{- \frac{4}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(125^{2 - \frac{4}{3}})$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(125^{2 \cdot \frac{3}{3} - \frac{4}{3}})$

Combine $2$ and $\frac{3}{3}$ .

$(125^{\frac{2 \cdot 3}{3} - \frac{4}{3}})$

Combine the numerators over the common denominator.

$(125^{\frac{2 \cdot 3 - 4}{3}})$

Simplify the numerator.

Multiply $2$ by $3$ .

$(125^{\frac{6 - 4}{3}})$

Subtract $4$ from $6$ .

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

Step 3

Remove parentheses.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$125^{2 - \frac{4}{3}}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$125^{2 \cdot \frac{3}{3} - \frac{4}{3}}$

Combine $2$ and $\frac{3}{3}$ .

$125^{\frac{2 \cdot 3}{3} - \frac{4}{3}}$

Combine the numerators over the common denominator.

$125^{\frac{2 \cdot 3 - 4}{3}}$

Simplify the numerator.

Multiply $2$ by $3$ .

$125^{\frac{6 - 4}{3}}$

Subtract $4$ from $6$ .

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

Step 4

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[3]{125^{2}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{125^{2}}$

Decimal Form:

$25$