Simplify 3^(2/5)*3^(-7/5)

$3^{\frac{2}{5}} \cdot 3^{- \frac{7}{5}}$

Multiply $3^{\frac{2}{5}}$ by $3^{- \frac{7}{5}}$ by adding the exponents.

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

$3^{\frac{2}{5} - \frac{7}{5}}$

Combine the numerators over the common denominator.

$3^{\frac{2 - 7}{5}}$

Subtract $7$ from $2$ .

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

Divide $- 5$ by $5$ .

$3^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$