How do you simplify #(c^3)^2(-3c^5)^2#?

1 Answer
Jan 7, 2017

Answer:

See full process explanation below

Explanation:

First, we simplify the terms within parenthesis using this rule for exponents:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(c^3)^2(-3c^5)^2 -> c^(3 xx 2) xx -3^2c^(5 xx 2) -> c^6 xx -27c^10#

We can then use this other rule of exponents to finalize the simplification:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b)#

#c^6 xx -27c^10 -> -27c^(6 + 10) -> -27c^16#