Question

(MC) Rewrite the rational exponent as a radical. (2 points) 5 to the 3 over 4 power, to the 2 over 3 power Select one: a. The cube root of 5 squared b. The twelfth root of 5 c. The square root of 5 d. The cube root of 5 the fourth power

Answer 1

`√(5)`

Explanation:

Given the expression;

`(5^{(3)/(4) })^{(2)/(3) }`

Using the law of indices that states;

`(a^m)^n = a^(mn)`

The expression becomes;

`(5^{(3)/(4) })^{(2)/(3) }\\= (5^{(3)/(4) * (2)/(3) })\\= 5^(6/12)\\= 5^(1/2)\\= √(5)`

Hence the correct answer is
`= √(5)`