# 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 }= (9^{3})^{1/3} = (9)^{3(1/3)} = 9

B) 27^{1/3 }= (3^{9})^{1/3 }= (3)^{9(1/3)} = 3

C) 27^{1/3 }= (3^{4})^{1/2} = (3)^{4(1/2)} = 9

D) 27^{1/3 }= (3^{3})^{1/3 }= (3)^{3(1/3)} = 3

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

## Answer: Option D is the right answer.

Go through the solution to understand better.

**Explanation:**

Let us solve (27)^{1/3 }step by step.

(27)^{1/3} = (3 × 3 × 3)^{1/3}

= (3^{3})^{1/3}

= 3^{(3 × 1/3)}

= 3^{1}

= 3

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

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