Solve (+7a^5b^4):(-7/8a^4b^5)

$$( + 7 a ^ { 5 } b ^ { 4 } ) : ( - \frac { 7 } { 8 } a ^ { 4 } b ^ { 5 } )$$

Evaluate

$$-\frac{8a}{b}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{7^{1}a^{5}b^{4}}{\left(-\frac{7}{8}\right)^{1}a^{4}b^{5}}$$

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

$$\frac{7^{1}}{\left(-\frac{7}{8}\right)^{1}}a^{5-4}b^{4-5}$$

Subtract 4 from 5.

$$\frac{7^{1}}{\left(-\frac{7}{8}\right)^{1}}a^{1}b^{4-5}$$

Subtract 5 from 4.

$$\frac{7^{1}}{\left(-\frac{7}{8}\right)^{1}}a\times \frac{1}{b}$$

Divide 7 by -\frac{7}{8} by multiplying 7 by the reciprocal of -\frac{7}{8}.

$$-8a\times \frac{1}{b}$$

Differentiate w.r.t. b

$$\frac{8a}{b^{2}}$$