Simplify the Radical Expression (m^(-5/8))(m^(3/8))

$(m^{- \frac{5}{8}}) (m^{\frac{3}{8}})$

Multiply $m^{- \frac{5}{8}}$ by $m^{\frac{3}{8}}$ by adding the exponents.

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

$m^{- \frac{5}{8} + \frac{3}{8}}$

Combine the numerators over the common denominator.

$m^{\frac{- 5 + 3}{8}}$

Add $- 5$ and $3$ .

$m^{\frac{- 2}{8}}$

Cancel the common factor of $- 2$ and $8$ .

Factor $2$ out of $- 2$ .

$m^{\frac{2 (- 1)}{8}}$

Cancel the common factors.

Factor $2$ out of $8$ .

$m^{\frac{2 \cdot - 1}{2 \cdot 4}}$

Cancel the common factor.

$m^{\frac{2 \cdot - 1}{2 \cdot 4}}$

Rewrite the expression.

$m^{\frac{- 1}{4}}$

Move the negative in front of the fraction.

$m^{- \frac{1}{4}}$

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

$\frac{1}{m^{\frac{1}{4}}}$