Question

Three claims are made about
2
5
3
.

Claim 1 states that
2
5
3
=
(
2
1
3
⋅
2
1
3
⋅
2
1
3
⋅
2
1
3
⋅
2
1
3
)
=
(
3
√
2
⋅
3
√
2
⋅
3
√
2
⋅
3
√
2
⋅
3
√
2
)
=
(
3
√
2
)
5
.

Claim 2 states that
2
5
3
=
(
2
×
2
×
2
×
2
×
2
)
(
2
×
2
×
2
)
=
2
5
2
3
=
2
2
.



Claim 3 states that
2
5
3
=
(
2
1
5
⋅
2
1
5
⋅
2
1
5
)
=
(
5
√
2
⋅
5
√
2
⋅
5
√
2
)
=
(
5
√
2
)
3
.


Which statements correctly analyze the claims made and identifies the part of the claim that is correct or incorrect? Select TWO that apply.


Claim 1 is correct and the work shown supports the claim.


Claim 1 is incorrect because
2
5
3
=
(
5
√
2
×
2
×
2
)
=
5
√
2
3
.



Claim 2 is correct and the work shown supports the claim.


Claim 3 is correct and the work shown supports the claim.


Claim 3 is incorrect because
2
5
3
=
(
2
⋅
2
⋅
2
⋅
2
⋅
2
)
1
3
=
3
√
2
5
.

Answer 1

Correct choices:

- Claim 1 is correct and the work shown supports the claim.
- 2^(5/3) = (2^(1/3))^5 = (∛2)^5, so writing it as five factors of 2^(1/3) is valid.

- Claim 3 is incorrect because 2^(5/3) = (2·2·2·2·2)^(1/3) = ³√(2^5).
- Claim 3's manipulation gives 2^(3/5), not 2^(5/3). The correct alternative form is (2^5)^(1/3) = ³√(2^5).