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.

Answer 1

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.