simplify. x^3/5x^2x^-1/2

would i first flip x^-1/2 to x^-2, therefore x^2 and x^-2 would cancel out,
so the answer would just be x^3/5?

or do i continue to change the exponent into 5 square root of x^3?

am i doing this right?

You can move 1/(x-1/2) = x1/2.

Therefore, you will have
X^3*X^1/2/5X^2 = X3/2/5 but check my work.

i don't really get what you are doing....where did the negative sign go?

To simplify the expression x^3/(5x^2x^(-1/2)), you are on the right track with flipping x^(-1/2) to x^(-2). However, you need to be careful with your exponent calculations.

Let's break down the steps:

Step 1: Flip the exponent of x^(-1/2) to x^(-2). This gives you x^3/(5x^2x^(-2)).

Step 2: Simplify the expression by combining the x terms in the denominator. Since the base (x) is the same, you can subtract the exponents.

x^2 * x^(-2) = x^(2 + (-2)) = x^0

Remember that any term with an exponent of 0 equals 1. So, x^0 simplifies to 1.

Now, we have x^3/(5 * 1) which is just x^3/5.

Therefore, the simplified expression is x^3/5.

You do not need to convert it to 5√x^3. It would only be necessary if there was a square root sign explicitly mentioned in the expression. But in this case, you can keep it as x^3/5.

So, your final answer is x^3/5.