Question

Which equation justifies why 9 ¹/₃ = 3√9?

a. (9 ¹/₃)³ = 9^(¹/₄ * 3) = 9
b. (9 ¹/₃)³ = 9^(¹/₃ + 3) = 9
c. (9 ¹/₃)³ = 9^(¹/₃ - 3) = 9
d. (9 ¹/₃)³ = 9^(3 - ¹/₃) = 9

Answer 1

The equation that justifies why 9 ¹/₃ = 3√9 is (9 ¹/₃)³ = 3³ = 27 = 9.

Step-by-step explanation:

To justify why 9 ¹/₃ = 3√9, we can use the rule for cubing exponentials. We can rewrite 9 ¹/₃ as (3³)¹/₃ = 3^(3 * ¹/₃) = 3.

Therefore, the correct equation is:

(9 ¹/₃)³ = 3³ = 27 = 9.