Answer
${x^{3}}{y^{9}}$
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:
$\dfrac{x^{(1/4)(12)}}{y^{(-3/4)(12)}}$
Multiply the exponents to simplify:
$\dfrac{x^{12/4}}{y^{-36/4}}=\dfrac{x^{3}}{y^{-9}}$
Simplified expressions cannot have negative exponents.
To get rid of the negative exponent, use the rule $a^{-m}=\frac{1}{a^m}$ to obtain:
$$\dfrac{x^3}{\frac{1}{y^9}}=x^3\cdot \dfrac{y^9}{1} ={x^{3}}{y^{9}}$$
