Question

Three students made claims about
y
3
2
.

Each student has provided his or her work to support their claim, as shown below.

Student 1 makes the claim that
y
3
2
=
(
y
1
3
⋅
y
1
3
)
=
(
3
√
y
⋅
3
√
y
)
=
(
3
√
y
)
2
.
Student 2 makes the claim that
y
3
2
=
(
y
⋅
y
⋅
y
)
1
2
=
(
√
y
⋅
y
⋅
y
)
=
(
√
y
3
)
.
Student 3 makes the claim that
y
3
2
=
(
y
1
2
⋅
y
1
2
⋅
y
1
2
)
=
(
√
y
⋅
√
y
⋅
√
y
)
=
(
√
y
)
3
.

Which statements correctly analyze the student's work and identify which part of his or her claim is correct or incorrect? Select TWO that apply.


Student 1 makes a correct claim and their work shown supports their claim.


Student 1 makes an incorrect claim because
y
3
2
=
(
3
√
y
2
)
. The exponent should be inside the radical.


Student 2 makes a correct claim and their work shown supports their claim.


Student 2 makes an incorrect claim because
y
3
2
=
(
3
√
y
2
)
.


Student 3 makes a correct claim and their work shown supports their claim.


Student 3 makes an incorrect claim because
y
3
2
=
(
√
y
3
)
.

Answer 1

Select: Student 2 makes a correct claim and their work shown supports their claim; and Student 3 makes a correct claim and their work shown supports their claim.

Explanation (brief):
- Student 1 is incorrect: (³√y)² = y^{2/3}, not y^{3/2}.
- Student 2’s conclusion √(y^3) is a correct form of y^{3/2} (y^{3/2} = (y^3)^{1/2}).
- Student 3’s work is also correct: (√y)^3 = (y^{1/2})^3 = y^{3/2}.