# How do you simplify (2^ { 4} ) ^ { 2} \times 2^ { 7}?

Dec 19, 2017

${\left({2}^{4}\right)}^{2} \cdot {2}^{7} = {2}^{15}$

#### Explanation:

One of our exponent rules deals with raising a power to another power. It is: ${\left({x}^{a}\right)}^{b} = {x}^{a b}$.
Therefore, ${\left({2}^{4}\right)}^{2} = {2}^{8}$.

Another exponent rule deals with multiplying a number with an exponent by the same number with a different exponent:
${x}^{a} \cdot {x}^{b} = {x}^{a + b}$.

Putting ${2}^{8}$ in for ${\left({2}^{4}\right)}^{2}$, the expression becomes
${2}^{8} \cdot {2}^{7} = {2}^{15}$.