Final answer:
The expression 64^(2/3) can be simplified to 16 using different methods of applying the properties of exponents, including rewriting the base as 4^3 or 8^2 and then applying the exponent 2/3.
Step-by-step explanation:
The expression 642/3 can be simplified in several ways using the properties of exponents. One method is to recognize that 64 is 43, so when we apply the exponent 2/3, we multiply the exponents (3×2/3) which simplifies to 42, or 16.
Another method is to first take the cube root of 64, which is 4, and then square that result, which again gives us 16.
Lastly, expressing 64 as 82 and then raising it to the power of 2/3 means we multiply the exponents (2×2/3) to get 84/3, which is the cube root of 8 raised to the fourth power, ultimately resulting in 16 as well.