Answer
$\dfrac{1}{{x^{6}}}$
Work Step by Step
When a fraction is raised to a power, the exponent applies to both the numerator as well as the denominator. Since both the numerator and denominator already contain exponents, we will multiply the exponents inside the parentheses with the one outside them. Let's rewrite the problem to reflect this:
$=\dfrac{\left(x^{-10}\right)^{2/5}}{\left(x^{5}\right)^{2/5}}\\
=\dfrac{x^{-10(2/5)}}{x^{5(2/5)}}\\
=\dfrac{x^{-4}}{x^{2}}$
Expressions in lowest terms do not have negative exponents. Use the rule $a^{-m}=\frac{1}{a^m}$ to obtain:
$=\dfrac{\frac{1}{x^4}}{x^2}\\
=\dfrac{1}{x^4(x^2)}\\
=\dfrac{1}{x^6}$
