64^2/3 Evaluate

To evaluate 64^2/3, we need to understand the concept of fractional exponents.

Definition of Fractional Exponents:
A fractional exponent is a way to express a root of a number. In general, if we have a number "a" raised to the power of "m/n" (where m and n are integers and n is not equal to zero), it can be written as the nth root of "a" raised to the power of "m".

Formula for Fractional Exponents:
a^(m/n) = (n√a)^m

Now let's apply this concept to evaluate 64^2/3.

Step 1: Convert the fractional exponent to its radical form.
The exponent 2/3 can be written as the cube root of 2, which we can represent as (2√).

Step 2: Apply the formula for fractional exponents.
64^(2/3) = (3√64)^2

Step 3: Simplify the expression inside the parentheses.
The cube root of 64 is 4 because 4 * 4 * 4 = 64.
So, (3√64) = 4.

Step 4: Substitute the simplified expression back into the original expression.
64^(2/3) = 4^2

Step 5: Evaluate the expression.
4^2 = 4 * 4 = 16

Final Answer:
64^(2/3) = 16

Explanation Recap:
- We started by converting the fractional exponent to its radical form.
- Then, we applied the formula for fractional exponents.
- Simplifying the expression inside the parentheses, we found that the cube root of 64 is 4.
- Substituting the simplified expression back into the original expression, we obtained 4^2.
- Evaluating the expression, we determined that 4^2 equals 16.
- Therefore, the final answer is 16.

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