Solve 5/4a^21/-20ab^4/-frac{1{4}ab^4}

$$\frac{ \frac{ \frac{ 5 }{ 4 } { a }^{ 21 } }{ -20a { b }^{ 4 } } }{ - \frac{ 1 }{ 4 } a { b }^{ 4 } }$$

Evaluate

$$\frac{a^{19}}{4b^{8}}$$

Solution Steps

Express \frac{\frac{\frac{5}{4}a^{21}}{-20ab^{4}}}{-\frac{1}{4}ab^{4}} as a single fraction.

$$\frac{\frac{5}{4}a^{21}}{-20ab^{4}\left(-\frac{1}{4}\right)ab^{4}}$$

Cancel out aa in both numerator and denominator.

$$\frac{\frac{5}{4}a^{19}}{-20\left(-\frac{1}{4}\right)b^{4}b^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\frac{5}{4}a^{19}}{-20\left(-\frac{1}{4}\right)b^{8}}$$

Multiply -20 and -\frac{1}{4} to get 5.

$$\frac{\frac{5}{4}a^{19}}{5b^{8}}$$

Differentiate w.r.t. b

$$-\frac{2a^{19}}{b^{9}}$$