sorry -- here it is

simplify this expression : (x^3 y)/(y^(1/2) x^(-2) ) when x is not = 0, and y is not equal to 0

thank you

WE know that [formula a^m/a^n=a^(m-n)]

where m>n it means in division when base (means 'a') are same with different power('m' and 'n') then powers are subtracted

x^3*y/[(y^1/2)*(x^-2)]

=x^3-(-2)*y^(1-1/2)

=x^3+2*y^1/2

=x^5*y^1/2

To simplify the expression (x^3 y)/(y^(1/2) x^(-2)), follow these steps:

Step 1: Simplify the powers of x.
Use the quotient rule of exponents, which states that when dividing powers with the same base, subtract the exponents. In this case, x^3 / x^(-2) can be simplified as follows:

x^3 / x^(-2) = x^(3 - (-2)) = x^5.

Step 2: Simplify the powers of y.
Use the power rule of exponents, which states that when raising a power to another power, multiply the exponents. In this case, y^(1/2) can be rewritten as y^(1 * 1/2) and simplified as follows:

y^(1 * 1/2) = y^(1/2).

Step 3: Divide the simplified expressions from steps 1 and 2.
Now, we have x^5 y / y^(1/2).

Step 4: Simplify the division of the y terms.
When dividing powers with the same base, subtract the exponents. In this case, y / y^(1/2) can be simplified as follows:

y / y^(1/2) = y^(1 - 1/2) = y^(1/2).

Step 5: Combine the simplified x and y expressions.
Now, we have x^5 y / y^(1/2) = x^5 y^(1/2).

Therefore, the simplified expression is x^5 y^(1/2).