# simplify:

x^(3/2)(x + x^(5/2) - x^2)

add exponents when multiplying. For instance, the first term above

x^3/2 * x=x^3/2 * x^2/2=x^5/2

add exponents when multiplying. For instance, the first term above

x^3/2 * x=x^3/2 * x^2/2=x^5/2

ok, so would the answer be x^3

no. I will be happy to critique your work.

no. I will be happy to critique your work.

x^(3/2)(x + x^(5/2) - x^2)

x^(5/2) + (x^4 - x^(7/2))

x^3

## Actually, the answer is x^5/2 + (x^4 - x^(7/2)).

To simplify the expression, we need to distribute the exponent of 3/2 to each term inside the parentheses.

x^(3/2)(x + x^(5/2) - x^2)

Using the rule of exponentiation, we multiply the exponents when raising one exponent to another one. In this case, x^(3/2) * x = x^(3/2 + 1) = x^(5/2).

So, the first term becomes x^(5/2).

The second and third terms do not have the same base, so we cannot simply add their exponents. Therefore, we leave them as separate terms.

The final simplified expression is x^(5/2) + (x^4 - x^(7/2)).