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

Answer:

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

Step-by-step 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

Answer 2

Answer:

Step-by-step explanation:

The answer is the first one.

$16^{\frac{1}{4}}$  simplifies down to

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

$2^{\frac{4}{4}}$  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:

$16^{\frac{1}{4}$  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:

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