# Can you simplify 2 to the third power times 2 to the fifth power?

Jan 25, 2016

Yes, the exponential property ${x}^{m}$(${x}^{n}$) = ${x}^{m + n}$ can be used to simplify this problem.

#### Explanation:

${2}^{3}$(${2}^{5}$)

=${2}^{5 + 3}$

= ${2}^{8}$

So, your problem can be simplified to ${2}^{8}$.

Beware that if you have an addition/subtraction (e.g ${2}^{5}$ + ${2}^{6}$) you cannot simplify with this rule. With division you can, but you subtract exponents instead of adding them. Also, this rule only works if the bases are equal

Practice exercises:

1. Simplify the following expressions. Beware of trick questions. When simplification is not possible, leave in exponential form.

a) ${3}^{4} / {3}^{2}$

b) ${3}^{4} \left({3}^{2}\right)$

c) ${3}^{4} - {3}^{2}$

d) ${3}^{4} / {3}^{-} 2$

e) ${3}^{2} \left({2}^{2}\right)$

1. Solve for x in ${4}^{3} / {4}^{x} = {4}^{10}$. Hint: think of integer addition/subtraction rules.