Question

Simplify each expression in the table below.
Select Option A or Option B.

Option A
Option B
(
x
3
y
−
2
)
4
x
12
y
8
x
7
y
2
(
3
x
2
y
−
3
)
2
9
x
4
y
6
3
x
4
y
6
(
7
−
3
7
3
)
4
1
1
7
24
(
x
2
y
−
3
z
)
2
x
4
z
2
y
6
x
4
y
z

Answer 1

I'll simplify each expression and indicate which option matches.

1) (x^3 y^−2)^4
- Simplify: x^(3·4) y^(−2·4) = x^12 y^(−8) = x^12 / y^8.
- Match: Option A.

2) (3 x^2 y^−3)^2
- Simplify: 3^2 x^(2·2) y^(−3·2) = 9 x^4 y^(−6) = 9 x^4 / y^6.
- Match: Option A.

3) (7^−3 / 7^3)^4
- Simplify inside: 7^(−3−3) = 7^(−6). Then ^4: 7^(−6·4) = 7^(−24) = 1 / 7^24.
- Match: Option A.

4) (x^2 y^−3 z)^2
- Simplify: x^(2·2) y^(−3·2) z^(1·2) = x^4 y^(−6) z^2 = x^4 z^2 / y^6.
- Match: Option A.

All four correct choices are Option A.