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

Answer:

$\sqrt{5}$

Step-by-step explanation:

Given the expression;

$(5^{\frac{3}{4} })^{\frac{2}{3} }$

Using the law of indices that states;

$(a^m)^n = a^{mn}$

The expression becomes;

$(5^{\frac{3}{4} })^{\frac{2}{3} }\\= (5^{\frac{3}{4} \times \frac{2}{3} })\\= 5^{6/12}\\= 5^{1/2}\\= \sqrt{5}$

Hence the correct answer is $= \sqrt{5}$