Question

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

Answer 1

`color(blue)(n^12)`

Explanation:

`PE MD AS`
(Order of Operations)
Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction

so the given is:

`n^3(n^3)^3`

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

Adding the exponents, just follow the rule of the exponents.

where: `(n^a)(n^a) = (n^(2a)) or (n^(a+a))`

`(n^3)^3 = (n^3)(n^3)(n^3) = n^9`

or

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

where: `(x^n)^m = x^(n*m) or x^(nm)`

`(n^3)^3 = n^9`

so we get, `n^9`

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

`n^3(n^9)`

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

where: `(n^a)(n^a) = (n^(2a)) or (n^(a+a))`

`n^3(n^9) = n^(3+9) = n^12`

so simplified answer is:

`color(blue)(n^12)`