Rational exponents 8^2/3?

did you mean

8^(2/3) ?
if so, then

8^(2/3) =( (8^(1/3) )^2
= 2^2
= 4

To evaluate the rational exponent 8^(2/3), we can follow two steps:

Step 1: Rewrite the rational exponent as a radical expression.
The numerator of the exponent, 2, represents the power, and the denominator, 3, represents the root. So, 8^(2/3) can be rewritten as the cube root of 8 raised to the power of 2, or ∛(8^2).

Step 2: Simplify the expression.
To simplify ∛(8^2), we need to determine the value of 8^2 and then find its cube root.

First, evaluate 8^2:
8^2 = 8 × 8 = 64.

Next, find the cube root of 64, which is the final step:
∛(64) = 4.

Therefore, 8^(2/3) is equal to 4.