Question

What is the simplest form of the number:
IMAGE

Answer 1

A. 2 8/5
B. 1024
C. 2 5/8
D. 2 1/10

Answer 2

@Light&Happiness

Answer 3

Another way to write √2 is 2^(1/2).
Similarly, another way write the eighth root of 2 is 2^(1/8).

But what happens when you multiply numbers with exponents that have the same base? You add them.

So that simplifies to 2^(1/2 + 1/8) = 2^(4/8 + 1/8) = 2^(5/8).

In other words, it's the eighth root of 2, to the fifth power.
Or equivalently, it's 2 to the fifth power, and then take the eighth root.

However, 2^5 = 32.

So, we could also that simplifies to the eighth root of 32.

Answer 4

that makes sense thank you for the clarification @TurtleMuffin

Answer 5

My pleasure!