Simplify (x^(2/5)y^(4/10))^-5

${(x^{\frac{2}{5}} y^{\frac{4}{10}})}^{- 5}$

Step 1

Cancel the common factor of $4$ and $10$ .

Factor $2$ out of $4$ .

${(x^{\frac{2}{5}} y^{\frac{2 (2)}{10}})}^{- 5}$

Cancel the common factors.

Factor $2$ out of $10$ .

${(x^{\frac{2}{5}} y^{\frac{2 \cdot 2}{2 \cdot 5}})}^{- 5}$

Cancel the common factor.

${(x^{\frac{2}{5}} y^{\frac{2 \cdot 2}{2 \cdot 5}})}^{- 5}$

Rewrite the expression.

${(x^{\frac{2}{5}} y^{\frac{2}{5}})}^{- 5}$

Step 2

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

$\frac{1}{{(x^{\frac{2}{5}} y^{\frac{2}{5}})}^{5}}$

Step 3

Simplify the denominator.

Apply the product rule to $x^{\frac{2}{5}} y^{\frac{2}{5}}$ .

$\frac{1}{{(x^{\frac{2}{5}})}^{5} {(y^{\frac{2}{5}})}^{5}}$

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

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

$\frac{1}{x^{\frac{2}{5} \cdot 5} {(y^{\frac{2}{5}})}^{5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{x^{\frac{2}{5} \cdot 5} {(y^{\frac{2}{5}})}^{5}}$

Rewrite the expression.

$\frac{1}{x^{2} {(y^{\frac{2}{5}})}^{5}}$

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

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

$\frac{1}{x^{2} y^{\frac{2}{5} \cdot 5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{x^{2} y^{\frac{2}{5} \cdot 5}}$

Rewrite the expression.

$\frac{1}{x^{2} y^{2}}$