Solve frac{3x^{0}y^{-4}}{3x^-1y^-3*4x^-1y^0}

$$\frac { 3 x ^ { 0 } y ^ { - 4 } } { 3 x ^ { - 1 } y ^ { - 3 } \cdot 4 x ^ { - 1 } y ^ { 0 } }$$

Evaluate

$$\frac{x^{2}}{4y}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and -1 to get -2.

$$\frac{3x^{0}y^{-4}}{3x^{-2}y^{-3}\times 4y^{0}}$$

To multiply powers of the same base, add their exponents. Add -3 and 0 to get -3.

$$\frac{3x^{0}y^{-4}}{3x^{-2}y^{-3}\times 4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{y^{-4}x^{0}}{4y^{-3}x^{-2}}$$

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

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

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

$$\frac{x^{2}}{4y^{1}}$$

Calculate y to the power of 1 and get y.

$$\frac{x^{2}}{4y}$$

Differentiate w.r.t. x

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