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
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.