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

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Answer 1 · 2018-01-01T20:23:07

$n^{12}$ $color(blue)(n^12)$

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

so the given is:

$n^{3} {(n^{3})}^{3}$ $n^3(n^3)^3$

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

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

where: $(n^{a}) (n^{a}) = (n^{2 a}) or (n^{a + a})$ $(n^a)(n^a) = (n^(2a)) or (n^(a+a))$

${(n^{3})}^{3} = (n^{3}) (n^{3}) (n^{3}) = n^{9}$ $(n^3)^3 = (n^3)(n^3)(n^3) = n^9$

or

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

where: ${(x^{n})}^{m} = x^{n \cdot m} or x^{n m}$ $(x^n)^m = x^(n*m) or x^(nm)$

${(n^{3})}^{3} = n^{9}$ $(n^3)^3 = n^9$

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

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

$n^{3} (n^{9})$ $n^3(n^9)$

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

where: $(n^{a}) (n^{a}) = (n^{2 a}) or (n^{a + a})$ $(n^a)(n^a) = (n^(2a)) or (n^(a+a))$

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

so simplified answer is:

$n^{12}$ $color(blue)(n^12)$

How do you simplify n3(n3)3n^3(n^3)^3?