Solve (frac{3x^{-7}y^-3}{6x^4y^-9})^-1

$$( \frac { 3 x ^ { - 7 } y ^ { - 3 } } { 6 x ^ { 4 } y ^ { - 9 } } ) ^ { - 1 }$$

Evaluate

$$\frac{2x^{11}}{y^{6}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\left(\frac{x^{-7}y^{-3}}{2y^{-9}x^{4}}\right)^{-1}$$

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

$$\left(\frac{x^{-7}y^{6}}{2x^{4}}\right)^{-1}$$

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

$$\left(\frac{y^{6}}{2x^{11}}\right)^{-1}$$

To raise \frac{y^{6}}{2x^{11}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{6}\right)^{-1}}{\left(2x^{11}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -1 to get -6.

$$\frac{y^{-6}}{\left(2x^{11}\right)^{-1}}$$

Expand \left(2x^{11}\right)^{-1}.

$$\frac{y^{-6}}{2^{-1}\left(x^{11}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and -1 to get -11.

$$\frac{y^{-6}}{2^{-1}x^{-11}}$$

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

$$\frac{y^{-6}}{\frac{1}{2}x^{-11}}$$

Differentiate w.r.t. x

$$\frac{22x^{10}}{y^{6}}$$