Marco and Paolo are working with expressions with rational exponents. Marco claims that 64^((2)/(3))=512. paolo claims that 64^((2)/(3))=16. which of them is correct? use the rational exponent property to justify your answer

Answer 1

To determine who is correct, let's simplify the given expressions using rational exponent properties.

We know that if we have a rational exponent, it can also be expressed as a radical. Specifically, a number raised to the power of p/q can be rewritten as the qth root of that number raised to the power of p.

In this case, we have 64 raised to the power of 2/3. Therefore, 64^(2/3) can also be expressed as the cubed root of 64 squared.

The cubed root of 64 is 4, because 4^3 = 64. Therefore, 64^(2/3) = (cubed root of 64)^2 = 4^2 = 16.

So Paolo is correct. 64^(2/3) is equal to 16, not 512.