Solve frac{60a^{8}*56b^{2}*a^-2}{12a^3*7b^6*5a^2}

$$\frac { 60 a ^ { 8 } \cdot 56 b ^ { 2 } \cdot a ^ { - 2 } } { 12 a ^ { 3 } \cdot 7 b ^ { 6 } \cdot 5 a ^ { 2 } }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and -2 to get 6.

$$\frac{60a^{6}\times 56b^{2}}{12a^{3}\times 7b^{6}\times 5a^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{60a^{6}\times 56b^{2}}{12a^{5}\times 7b^{6}\times 5}$$

Cancel out 5\times 7\times 12b^{2}a^{5} in both numerator and denominator.

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

Differentiate w.r.t. b

$$-\frac{32a}{b^{5}}$$