Answer: 16z⁴
Step-by-step explanation:
First, we distribute the powers on the outside of the parenthesis to the inside of the parenthesis using [tex](ab)^{n} = a^{n}b^{n}[/tex]:
[tex]\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}[/tex]
Then, we can use [tex](a^{n})^m = a^{nm}[/tex] to simplify the numerator:
[tex]\frac{16(z^2)^3}{z^2} = \frac{16z^{2*3}}{z^2} =\frac{16z^{6}}{z^2}[/tex]
Finally, we can use [tex]\frac{a^n}{a^m} =a^{m-n}[/tex] to simplify further:
[tex]\frac{16z^{6}}{z^2} = 16z^{6-2} = 16z^4[/tex]
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
