Solve 6x^3y^-4/2x^-7y^3x/2

$$\frac{ 6 { x }^{ 3 } { y }^{ -4 } }{ 2 { x }^{ -7 } { y }^{ 3 } } \frac{ x }{ 2 }$$

Evaluate

$$\frac{3x^{11}}{2y^{7}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3y^{-4}x^{3}}{x^{-7}y^{3}}\times \frac{x}{2}$$

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

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

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

$$\frac{3x^{10}}{y^{7}}\times \frac{x}{2}$$

Multiply \frac{3x^{10}}{y^{7}} times \frac{x}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{10}x}{y^{7}\times 2}$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\frac{3x^{11}}{y^{7}\times 2}$$

Differentiate w.r.t. x

$$\frac{33x^{10}}{2y^{7}}$$