Which of the following shows the correct steps to find the value of 27 to the power of 1 over 3?
A) 27^1/3 = (9³)^1/3 = (9)^3(1/3) = 9
B) 27^1/3 = (3⁹)^1/3 = (3)^9(1/3) = 3
C) 27^1/3 = (3⁴)^1/2 = (3)^4(1/2) = 9
D) 27^1/3 = (3³)^1/3 = (3)^3(1/3) = 3

Solution:

Exponential terms can be easily broken down using factorization of the terms into simple factors.

Let us solve (27)^1/3 step by step.

(27)^1/3 = (3 × 3 × 3)^1/3 

= (3³)^1/3

= 3^{(3 × 1/3)}

= 3¹

= 3

Thus, option D matches both the L.H.S and the R.H.S, and is, therefore, the correct answer.

Which of the following shows the correct steps to find the value of 27 to the power of 1 over 3?

Summary:

Option D is the right answer.