Correct arrangement of the question is;
Rewrite the rational exponent as a radical: five to the three fourths power all raised to the two thirds power
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:
Option C) the square root of 5
Explanation:
We are given: five to the three fourths power all raised to the two thirds power
Translating that statement means 5 is raised to ¾ raised to ⅔.
In indices, when we have two powers attached to a number, the two powers will multiply each other.
Thus, 5 is raised to; ⅔ × ¾ = 2/4 = ½
Thus, 5 is raised to power ½.
Now, when a number is raised to the power ½, it is said to be square root of that number.
Thus, the right answer is square root of five.