Amelia claims that (9c4)3−−−−−√=27c8 Is Amelia correct? (2 points) Explain how you know she is correct or incorrect. (4 points)

Answer 1

To determine if Amelia is correct, we need to simplify both sides of the equation:

(9c4)^(3/2) = 27c^8

First, let's simplify the left side using the exponent property that states (a^m)^n = a^(m*n):

(9c4)^(3/2) = 9^((3/2) * (c4) * (3/2))
= 9^(9/2 * c * 12/2)
= 9^(27/2c)
= (sqrt(9))^27c
= 3^27c

Now, let's simplify the right side by raising 27 to the power of 8:

27c^8 = (3^3c)^8
= 3^(3c * 8)
= 3^(24c)

We can see that the left side is equal to (3^27c) while the right side is equal to (3^24c). Therefore, Amelia's claim that (9c4)^(3/2) = 27c^8 is incorrect. The correct equation should be (9c4)^(3/2) = (27c^8)^(3/2).