Solve 6g^2r^3/8g^4r^6

$$\frac { 6 g ^ { 2 } r ^ { 3 } } { 8 g ^ { 4 } r ^ { 6 } }$$

Evaluate

$$\frac{3}{4g^{2}r^{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}g^{2}r^{3}}{8^{1}g^{4}r^{6}}$$

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

$$\frac{6^{1}}{8^{1}}g^{2-4}r^{3-6}$$

Subtract 4 from 2.

$$\frac{6^{1}}{8^{1}}g^{-2}r^{3-6}$$

Subtract 6 from 3.

$$\frac{6^{1}}{8^{1}}\times \frac{1}{g^{2}}r^{-3}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}\times \frac{1}{g^{2}}\times \frac{1}{r^{3}}$$

Differentiate w.r.t. r

$$-\frac{9}{4g^{2}r^{4}}$$