How much is 8 to the power of 2/3?

Power, in exponents, is defined as the total number of times we use the number in a multiplication. For example, 2 to the power 3 means 2 is multiplied 3 times.

Answer: 8 to the power of 2/3 is 4.

Let's see the solution step by step.

Explanation:

We have 8 to the power of 2/3 or 8^(2/3).

First, we will rewrite 8 as 2³.

8^{(2/3) =} 2^3(2/3)

We will apply the rules of exponents and multiply the exponents, (a^m)ⁿ = a^mn.

8^{(2/3) =} 2^3(2/3) = 2^3 × (2/3)

Now, we will cancel the common factor 3 which will result in 2² = 4

Thus, 8 to the power of 2/3 is 4.