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 rational exponent property to justify you answer.
To determine who is correct, let's simplify the given expression using the rational exponent property.
Remember that in general, the rational exponent property states that: a^(m/n) = (a^m)^(1/n)
In this case, we have 64^(2/3). We can rewrite this as (64^2)^(1/3).
Using the rational exponent property, (64^2)^(1/3) simplifies to 4096^(1/3).
Now we need to evaluate 4096^(1/3). This can be done by finding the cube root of 4096.
The cube root of 4096 is 16. So,
4096^(1/3) = 16
Therefore, Paolo is correct. The expression 64^(2/3) is equal to 16, not 512.