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

1 Answer
Jan 1, 2018

Answer:

#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)#