Solve 27u^2v^3/118u^4v^5=

$$\frac { 27 u ^ { 2 } v ^ { 3 } } { 118 u ^ { 4 } v ^ { 5 } } =$$

Evaluate

$$\frac{27}{118\left(uv\right)^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{27^{1}u^{2}v^{3}}{118^{1}u^{4}v^{5}}$$

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

$$\frac{27^{1}}{118^{1}}u^{2-4}v^{3-5}$$

Subtract 4 from 2.

$$\frac{27^{1}}{118^{1}}u^{-2}v^{3-5}$$

Subtract 5 from 3.

$$\frac{27^{1}}{118^{1}}\times \frac{1}{u^{2}}v^{-2}$$

Divide 27 by 118.

$$\frac{27}{118}\times \frac{1}{u^{2}}\times \frac{1}{v^{2}}$$

Differentiate w.r.t. v

$$-\frac{27}{59u^{2}v^{3}}$$