Question

Please help me with this question #20

Answer 1

Answer:

  answers C and D are both correct. (I consider D to be "simpler.")

Step-by-step explanation:

By the rules of exponents ...

  (a^b)^c = a^(b·c)

Here, we have a=-3, b=2. c=3, so ...

  ((-3)^2)^3 = (-3)^(2·3) = (-3)^6

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Consider further that ...

  -3 = (-1)(3)

and another rule of exponents tells you ...

  (a·b)^c = (a^c)·(b^c)

so our previous simplified result can also be written as ...

  (-3)^6 = ((-1)·(3))^6 = (-1)^6·(3)^6 = 1·(3)^6 = (3)^6

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I find it hard to tell just how "simplified" your answer key may want the answer to be. Of course, the simplest possible form is 729.