Simplify the Radical Expression a^(2/5)*a^-3

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

Step 1

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

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

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

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Combine $- 3$ and $\frac{5}{5}$ .

$a^{\frac{2}{5} + \frac{- 3 \cdot 5}{5}}$

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 3$ by $5$ .

$a^{\frac{2 - 15}{5}}$

Subtract $15$ from $2$ .

$a^{\frac{- 13}{5}}$

Move the negative in front of the fraction.

$a^{- \frac{13}{5}}$

Step 2

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

$\frac{1}{a^{\frac{13}{5}}}$