# How do you simplify (m^2p^5)^3?

Oct 22, 2017

${m}^{6} {p}^{15}$

#### Explanation:

$\textcolor{b l u e}{\text{The teaching bit}}$

By example suppose we had the variable $a$

This may be written as ${a}^{1}$

Now compare to $a \times a \times a = {a}^{3} = {a}^{1 + 1 + 1}$

So if we had ${\left({a}^{2}\right)}^{3}$ this would be the same as ${a}^{2 \times 3} = {a}^{6}$

If you have doubts! : ${2}^{2} \times {2}^{2} = 4 \times 4 = 16 = {2}^{2 \times 2} = 16$
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$\textcolor{b l u e}{\text{Answering the question}}$

Using the above approach we have:

$\left({m}^{2 \times 3}\right) \times \left({p}^{5 \times 3}\right)$

${m}^{6} {p}^{15}$