Question

(04.01)

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

Group of answer choices

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

Explanation:

The answer is the first one.

`16^{(1)/(4)}` simplifies down to

`(2^4)^{(1)/(4)}` The power to power rule is that you multiply the exponents together:

`2^{(4)/(4)}` which is
`2^1` which is 2

I'm assuming that you are also working with radicals (since radicals and exponents are inverses of each other). The way to write this is as a radical and simplify it is:

`16^{(1)/(4)` as a radical is

`\sqrt[4]{16^1}`

To simplify, try to write the radicand (the number under the square root) so it's a number with a power that matches the index (the number in the "arm" of the radical sign. Our index is a 4).

16 is the same as 2⁴:

`\sqrt[4]{2^4}`

The power on the 2 is a 4, which is the same as the index. When the power matches the index, you pull out the base as a single number:

`\sqrt[4]{2^4}=2`

Answer 2

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

Explanation:

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)^1/4 = (2^4)^1/4

4 cancels 4

2^1 = 2