Simplify (125^(1/3))/(125^(2/3))

$\frac{125^{\frac{1}{3}}}{125^{\frac{2}{3}}}$

Step 1

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

$\frac{1}{125^{\frac{2}{3}} \cdot 125^{- \frac{1}{3}}}$

Step 2

Multiply $125^{\frac{2}{3}}$ by $125^{- \frac{1}{3}}$ by adding the exponents.

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

$\frac{1}{125^{\frac{2}{3} - \frac{1}{3}}}$

Combine the numerators over the common denominator.

$\frac{1}{125^{\frac{2 - 1}{3}}}$

Subtract $1$ from $2$ .

$\frac{1}{125^{\frac{1}{3}}}$

Step 3

Simplify the denominator.

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

$\frac{1}{{(5^{3})}^{\frac{1}{3}}}$

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

$\frac{1}{5^{3 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{5^{3 (\frac{1}{3})}}$

Rewrite the expression.

$\frac{1}{5^{1}}$

Evaluate the exponent.

$\frac{1}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$