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

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Answer 1 · 2018-01-01T20:23:07

$color(blue)(n^12)$

$PE MD AS$
(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:

$color(blue)(n^12)$

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