Solve frac{x^{-3}y^{2}}{2xy^-3}div4x^2y^-5/6xy^3

$$\frac { x ^ { - 3 } y ^ { 2 } } { 2 x y ^ { - 3 } } \div \frac { 4 x ^ { 2 } y ^ { - 5 } } { 6 x y ^ { 3 } }$$

Evaluate

$$\frac{3y^{13}}{4x^{5}}$$

Solution Steps

Divide \frac{x^{-3}y^{2}}{2xy^{-3}} by \frac{4x^{2}y^{-5}}{6xy^{3}} by multiplying \frac{x^{-3}y^{2}}{2xy^{-3}} by the reciprocal of \frac{4x^{2}y^{-5}}{6xy^{3}}.

$$\frac{x^{-3}y^{2}\times 6xy^{3}}{2xy^{-3}\times 4x^{2}y^{-5}}$$

Cancel out 2x in both numerator and denominator.

$$\frac{3x^{-3}y^{2}y^{3}}{4y^{-5}y^{-3}x^{2}}$$

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

$$\frac{3x^{-3}y^{3}y^{10}}{4x^{2}}$$

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

$$\frac{3y^{3}y^{10}}{4x^{5}}$$

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$\frac{3y^{13}}{4x^{5}}$$

Differentiate w.r.t. x

$$-\frac{15y^{13}}{4x^{6}}$$