Answer
$\dfrac{y^{5}}{x^{10}}$
Work Step by Step
Here, we have a fraction raised to a power. This means that the exponent applies to both the numerator and the denominator.
When we raise a power to a power, we simply multiply the two powers together:
$\dfrac{x^{(-2/3)(15)}}{y^{(-1/3)(15)}}=\dfrac{x^{-30/3}}{y^{-15/3}}=\dfrac{x^{-10}}{y^{-5}}$
Simplified expressions cannot have negative exponents.
To get rid of the negative exponent, use the rule $a^{-m}=\frac{1}{a^m}$ to obtain:
$$\dfrac{x^{-10}}{y^{-5}}=\dfrac{\frac{1}{x^{10}}}{\frac{1}{y^5}}=\frac{1}{x^{10}} \cdot \frac{y^{5}}{1}=\dfrac{y^5}{x^{10}}$$
