Question

Which is equivalent to:
(
x
5
y
2
z
−
3
x
3
y
−
2
z
−
2
)
3
?
Select one answer
A
x
6
y
12
z
3

B
x
5
y
7
z
2

C
x
2
y
4
z

D
x
5
y
7
z
4

E
x
5
y
7
z

F
1

Answer 1

Interpret the expression as ((x^5 y^2 z^-3) ÷ (x^3 y^-2 z^-2))^3.

Inside the parentheses subtract exponents:
x^(5-3) y^(2-(-2)) z^(-3-(-2)) = x^2 y^4 z^-1 = x^2 y^4 / z.

Raise to the 3rd power:
(x^2 y^4 / z)^3 = x^6 y^12 / z^3 = x^6 y^12 z^-3.

Answer: A.