Simplify ((a^(1/2))/b)^(-2/5)

${(\frac{a^{\frac{1}{2}}}{b})}^{- \frac{2}{5}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{b}{a^{\frac{1}{2}}})}^{\frac{2}{5}}$

Step 2

Apply the product rule to $\frac{b}{a^{\frac{1}{2}}}$ .

$\frac{b^{\frac{2}{5}}}{{(a^{\frac{1}{2}})}^{\frac{2}{5}}}$

Step 3

Multiply the exponents in ${(a^{\frac{1}{2}})}^{\frac{2}{5}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{b^{\frac{2}{5}}}{a^{\frac{1}{2} \cdot \frac{2}{5}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{b^{\frac{2}{5}}}{a^{\frac{1}{2} \cdot \frac{2}{5}}}$

Rewrite the expression.

$\frac{b^{\frac{2}{5}}}{a^{\frac{1}{5}}}$