Solve frac{(x^{3})^{-4}}{2x^-1y^3*2x^-2y^4}

$$\frac { ( x ^ { 3 } ) ^ { - 4 } } { 2 x ^ { - 1 } y ^ { 3 } \cdot 2 x ^ { - 2 } y ^ { 4 } }$$

Evaluate

$$\frac{1}{4y^{7}x^{9}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$\frac{x^{-12}}{2x^{-1}y^{3}\times 2x^{-2}y^{4}}$$

To multiply powers of the same base, add their exponents. Add -1 and -2 to get -3.

$$\frac{x^{-12}}{2x^{-3}y^{3}\times 2y^{4}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{x^{-12}}{2x^{-3}y^{7}\times 2}$$

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

$$\frac{1}{2\times 2y^{7}x^{9}}$$

Multiply 2 and 2 to get 4.

$$\frac{1}{4y^{7}x^{9}}$$

Differentiate w.r.t. x

$$-\frac{9}{4y^{7}x^{10}}$$