# How to simplify this?

## ${\left(16 {p}^{16}\right)}^{\frac{1}{4}}$

Oct 26, 2016

${\left(16 {p}^{16}\right)}^{\frac{1}{4}} = 2 {p}^{4}$

#### Explanation:

We will apply the following rules of exponents:

• ${\left(a b\right)}^{x} = {a}^{x} {b}^{x}$
• ${\left({a}^{x}\right)}^{y} = {a}^{x y}$

With those, and observing that $16 = {2}^{4}$, we have

${\left(16 {p}^{16}\right)}^{\frac{1}{4}} = {16}^{\frac{1}{4}} {\left({p}^{16}\right)}^{\frac{1}{4}}$

$= {\left({2}^{4}\right)}^{\frac{1}{4}} {\left({p}^{16}\right)}^{\frac{1}{4}}$

$= {2}^{4 \cdot \frac{1}{4}} {p}^{16 \cdot \frac{1}{4}}$

$= {2}^{1} {p}^{4}$

$= 2 {p}^{4}$