# How do you simplify n^3(n^3)^3?

Jan 1, 2018

$\textcolor{b l u e}{{n}^{12}}$

#### Explanation:

$P E M D A S$
(Order of Operations)
Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction

so the given is:

${n}^{3} {\left({n}^{3}\right)}^{3}$

First, we need to evaluate the term in a parenthesis,

where: $\left({n}^{a}\right) \left({n}^{a}\right) = \left({n}^{2 a}\right) \mathmr{and} \left({n}^{a + a}\right)$

${\left({n}^{3}\right)}^{3} = \left({n}^{3}\right) \left({n}^{3}\right) \left({n}^{3}\right) = {n}^{9}$

or

(Multiplying the exponent to exponent just follow the rule of the exponents).

where: ${\left({x}^{n}\right)}^{m} = {x}^{n \cdot m} \mathmr{and} {x}^{n m}$

${\left({n}^{3}\right)}^{3} = {n}^{9}$

so we get, ${n}^{9}$

plugging the simplified to term to the first term, we get,

${n}^{3} \left({n}^{9}\right)$

same rule, we just need to add the exponents, following the rule of:

where: $\left({n}^{a}\right) \left({n}^{a}\right) = \left({n}^{2 a}\right) \mathmr{and} \left({n}^{a + a}\right)$

${n}^{3} \left({n}^{9}\right) = {n}^{3 + 9} = {n}^{12}$

$\textcolor{b l u e}{{n}^{12}}$