Answer: 16z⁴
Step-by-step explanation:
First, we distribute the powers on the outside of the parenthesis to the inside of the parenthesis using \((ab)^{n} = a^{n}b^{n}\):
\(\frac{(4z^{2})^3}{(2z)^2} = \frac{4^3(z^2)^{3} }{2^2z^2} = \frac{64(z^2)^{3}}{4z^2} = \frac{16(z^2)^3}{z^2}\)
Then, we can use \((a^{n})^m = a^{nm}\) to simplify the numerator:
\(\frac{16(z^2)^3}{z^2} = \frac{16z^{2*3}}{z^2} =\frac{16z^{6}}{z^2}\)
Finally, we can use \(\frac{a^n}{a^m} =a^{m-n}\) to simplify further:
\(\frac{16z^{6}}{z^2} = 16z^{6-2} = 16z^4\)
Therefore, we have a final answer of 16z⁴.
I hope this helps! Good luck with your studies as well, and have a great day.
colemaikell08
