Solve (2a^6b^7/4a^2b^5)

$$( \frac { 2 a ^ { 6 } b ^ { 7 } } { 4 a ^ { 2 } b ^ { 5 } } )$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}a^{6}b^{7}}{4^{1}a^{2}b^{5}}$$

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

$$\frac{2^{1}}{4^{1}}a^{6-2}b^{7-5}$$

Subtract 2 from 6.

$$\frac{2^{1}}{4^{1}}a^{4}b^{7-5}$$

Subtract 5 from 7.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Differentiate w.r.t. b

$$ba^{4}$$