# How do you simplify  (3/y)^4?

Aug 30, 2016

You can simplify it to $\left({3}^{4} / {y}^{4}\right)$ or $\left(\frac{81}{y} ^ 4\right)$

#### Explanation:

So one of the properties of exponents is that they distribute.
For example, if you have ${\left(x\right)}^{3}$, it distributes to be ${x}^{3}$.

In a better example, ${\left(\frac{2}{3}\right)}^{2}$ is equal to $\left({2}^{2} / {3}^{2}\right)$. This is equal to $\left(\frac{2 \cdot 2}{3 \cdot 3}\right)$ and $\left(\frac{4}{9}\right)$.

So, taking your problem into my hands, we have ${\left(\frac{3}{y}\right)}^{4}$ which can be simplified to $\left({3}^{4} / {y}^{4}\right)$ and that to $\left(\frac{3 \cdot 3 \cdot 3 \cdot 3}{y}\right)$ and that to $\left(\frac{81}{y} ^ 4\right)$.

If an exponent is outside of a fraction, it distributes to both the numerator and denominator.

Have a good day!