Solve 4a^6/b^8:(8a^3b^2)

$$\frac { 4 a ^ { 6 } } { b ^ { 8 } } : ( 8 a ^ { 3 } b ^ { 2 } )$$

Evaluate

$$\frac{a^{3}}{2b^{10}}$$

Solution Steps

Express \frac{\frac{4a^{6}}{b^{8}}}{8a^{3}b^{2}} as a single fraction.

$$\frac{4a^{6}}{b^{8}\times 8a^{3}b^{2}}$$

Cancel out 4a^{3} in both numerator and denominator.

$$\frac{a^{3}}{2b^{2}b^{8}}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\frac{a^{3}}{2b^{10}}$$

Differentiate w.r.t. b

$$-\frac{5a^{3}}{b^{11}}$$