Final answer:
To rewrite 64^(1/3) without using rational exponents, we find the cube root of 64 which is 4 since 4 x 4 x 4 equals 64. Therefore, the simplified expression is 4.
Step-by-step explanation:
The student has asked to rewrite the expression 64(1/3) without using rational exponents, and to simplify the expression if possible. This process involves finding the cube root of 64, since the exponent 1/3 corresponds to the cube root. In this case, 64 is a perfect cube because it can be expressed as 43.
To rewrite without the rational exponent, we can therefore describe 64(1/3) as the cube root of 64. This means we are looking for a number that, when multiplied by itself three times (cubed), gives us 64. We know that 4 x 4 x 4 equals 64, so the cube root of 64 is 4. Thus, 64(1/3) simplifies to 4.