Evaluate 8^(2/3).

Evaluate 8^(2/3).

• A. 8
• B. 4
• C. 2
• D. sqrt(8)

Answer: (B)

Fractional exponents encode a two-step process: the denominator tells you which root to take, and the numerator tells you what power to apply after the root. For a positive base, you can do these steps in either order. So 8^(2/3) means take the cube root of 8 and then square, or equivalently square 8 and then take the cube root. The cube root of 8 is 2, and squaring gives 4. Alternatively, 8^2 is 64, and the cube root of 64 is also 4. Therefore, the value is 4.

Fractional exponents encode a two-step process: the denominator tells you which root to take, and the numerator tells you what power to apply after the root. For a positive base, you can do these steps in either order.

So 8^(2/3) means take the cube root of 8 and then square, or equivalently square 8 and then take the cube root. The cube root of 8 is 2, and squaring gives 4. Alternatively, 8^2 is 64, and the cube root of 64 is also 4. Therefore, the value is 4.