Solve (9x^3y/y^-3)^1/2

$$( \frac { 9 x ^ { 3 } y } { y ^ { - 3 } } ) ^ { 1 / 2 }$$

Evaluate

$$3x^{\frac{3}{2}}y^{2}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(9x^{3}y^{4}\right)^{\frac{1}{2}}$$

Expand \left(9x^{3}y^{4}\right)^{\frac{1}{2}}.

$$9^{\frac{1}{2}}\left(x^{3}\right)^{\frac{1}{2}}\left(y^{4}\right)^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$9^{\frac{1}{2}}x^{\frac{3}{2}}\left(y^{4}\right)^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{1}{2} to get 2.

$$9^{\frac{1}{2}}x^{\frac{3}{2}}y^{2}$$

Calculate 9 to the power of \frac{1}{2} and get 3.

$$3x^{\frac{3}{2}}y^{2}$$

Differentiate w.r.t. x

$$\frac{9\sqrt{x}y^{2}}{2}$$