Evaluate (11^(2/5))/(11^(4/5))

$\frac{11^{\frac{2}{5}}}{11^{\frac{4}{5}}}$

Step 1

Move $11^{\frac{2}{5}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{11^{\frac{4}{5}} \cdot 11^{- \frac{2}{5}}}$

Step 2

Multiply $11^{\frac{4}{5}}$ by $11^{- \frac{2}{5}}$ by adding the exponents.

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

$\frac{1}{11^{\frac{4}{5} - \frac{2}{5}}}$

Combine the numerators over the common denominator.

$\frac{1}{11^{\frac{4 - 2}{5}}}$

Subtract $2$ from $4$ .

$\frac{1}{11^{\frac{2}{5}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{11^{\frac{2}{5}}}$

Decimal Form:

$0.38321537 \dots$