Question

Which of the following shows the correct steps to find the value of 16 to the power of 1 over 4?

16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2
16 to the power of 1 over 4 equals 4 to the power of 4 to the power of 1 over 4 equals 4 to the power of 4 multiplied by 1 over 4 equals 4
16 to the power of 1 over 4 equals 2 to the power of 8 to the power of 1 over 4 equals 8 to the power of 8 multiplied by 1 over 4 equals 4
16 to the power of 1 over 4 equals 8 to the power of 2 to the power of 1 over 4 equals 2 to the power of 2 multiplied by 1 over 4 equals 8

Answer 1

Ans. 16 to the power of 1 over 4 equals 4 to the power of 4 to the power of 1 over 4 equals 4 to the power of 4 multiplied by 1 over 4 equals 4

Answer 2

Option A is correct.

Value of 16 to the power of 1 over 4 equals to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplies by 1 over 4 equal 2.

Explanation:

To find the value of: 16 to the power of 1 over 4.

`16^{(1)/(4)}`

we can write 16 as:

`16 = 2 \cdot 2 \cdot 2 \cdot 2 = 2^4`

⇒
`(2^4)^{(1)/(4)}`

⇒
`(2)^{4 \cdot (1)/(4)}` [∴
`(a^n)^m = a^(nm)`]

⇒2

Hence, the value of
`16^{(1)/(4)}` is, 2.

Therefore, the value of 16 to the power of 1 over 4 equals to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplies by 1 over 4 equal 2.