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

Answer 1

Genesis Allen

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#

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Answer 2

Nathan Axel

To simplify (c^3)^2(-3c^5)^2, first simplify each expression inside the parentheses, then apply the rules of exponents. (c^3)^2 becomes c^(32) which is c^6. (-3c^5)^2 becomes (-3)^2(c^5)^2 which is 9c^(52) which simplifies to 9c^10. Finally, multiply the simplified expressions: c^6 * 9c^10 = 9c^(6+10) = 9c^16.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.