Evaluate (7^(1/5))/(7^(3/5))

$\frac{7^{\frac{1}{5}}}{7^{\frac{3}{5}}}$

Step 1

Move $7^{\frac{1}{5}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{7^{\frac{3}{5}} \cdot 7^{- \frac{1}{5}}}$

Step 2

Multiply $7^{\frac{3}{5}}$ by $7^{- \frac{1}{5}}$ by adding the exponents.

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

$\frac{1}{7^{\frac{3}{5} - \frac{1}{5}}}$

Combine the numerators over the common denominator.

$\frac{1}{7^{\frac{3 - 1}{5}}}$

Subtract $1$ from $3$ .

$\frac{1}{7^{\frac{2}{5}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7^{\frac{2}{5}}}$

Decimal Form:

$0.45915654 \dots$