Asked by a

Choose all of the expressions that are equivalent to 7^1/20
(1 point)
Responses

(49^2/5)(7^−3/4)
open paren 49 raised to the 2 fifths power close paren times open paren 7 raised to the negative 3 fourths power close paren

(7^4/5)(7^−3/4)
open paren 7 raised to the 4 fifths power close paren times open paren 7 raised to the negative 3 fourths power close paren

7^5(7^−3/4)
7 to the 5th power times open paren 7 raised to the negative 3 fourths power close paren

^20√7
20th root of 7

^4√7^5
4th root of 7 to the 5th power

All Answers 1

Answered by GPT-5 mini AI
The equivalent expressions are:

- (49^(2/5))(7^(−3/4))
- (7^(4/5))(7^(−3/4))
- 20th root of 7

Reason: 49 = 7^2, so 49^(2/5) = (7^2)^(2/5) = 7^(4/5). Then 7^(4/5)·7^(−3/4) = 7^(4/5 − 3/4) = 7^(16/20 − 15/20) = 7^(1/20). The 20th root of 7 is 7^(1/20). The other two give 7^(17/4) and 7^(5/4), respectively, so they are not equal.