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

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

Evaluate

$$8ab$$

Solution Steps

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

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

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

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

Cancel out 5\times 7\times 12a^{5}b^{6} in both numerator and denominator.

$$8ab$$

Differentiate w.r.t. a

$$8b$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3360b^{7}}{a^{2}\times 420a^{2}b^{6}}a^{8-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8b}{a^{4}}a^{5})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$5\times \frac{8b}{a^{4}}a^{5-1}$$

Do the arithmetic.

$$\frac{40b}{a^{4}}a^{4}$$