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

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Answer 1 · 2017-01-07T18:20:25

See full process explanation below

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:

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

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

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