Solve frac{2a^{2}b^{3}c^-5}{10a^-3b^-1c^2}

$$\frac { 2 a ^ { 2 } b ^ { 3 } c ^ { - 5 } } { 10 a ^ { - 3 } b ^ { - 1 } c ^ { 2 } }$$

Evaluate

$$\frac{b^{4}a^{5}}{5c^{7}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{c^{-5}a^{2}b^{3}}{5a^{-3}\times \frac{1}{b}c^{2}}$$

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

$$\frac{c^{-5}b^{4}a^{5}}{5c^{2}}$$

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

$$\frac{b^{4}a^{5}}{5c^{7}}$$

Differentiate w.r.t. a

$$\frac{\left(ab\right)^{4}}{c^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2b^{3}}{c^{5}\times \frac{10c^{2}}{b}}a^{2-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{b^{4}}{5c^{7}}a^{5})$$

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}.

$$5\times \frac{b^{4}}{5c^{7}}a^{5-1}$$

Do the arithmetic.

$$\frac{b^{4}}{c^{7}}a^{4}$$