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