Solve 2a^6b^2/6a^5b^4

$$\frac { 2 a ^ { 6 } b ^ { 2 } } { 6 a ^ { 5 } b ^ { 4 } }$$

Evaluate

$$\frac{a}{3b^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}a^{6}b^{2}}{6^{1}a^{5}b^{4}}$$

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

$$\frac{2^{1}}{6^{1}}a^{6-5}b^{2-4}$$

Subtract 5 from 6.

$$\frac{2^{1}}{6^{1}}a^{1}b^{2-4}$$

Subtract 4 from 2.

$$\frac{2^{1}}{6^{1}}ab^{-2}$$

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

$$\frac{1}{3}a\times \frac{1}{b^{2}}$$

Differentiate w.r.t. b

$$-\frac{2a}{3b^{3}}$$