Solve 42a^5b^3/35a^2b^2

$$\frac { 42 a ^ { 5 } b ^ { 3 } } { 35 a ^ { 2 } b ^ { 2 } }$$

Evaluate

$$\frac{6ba^{3}}{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{42^{1}a^{5}b^{3}}{35^{1}a^{2}b^{2}}$$

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

$$\frac{42^{1}}{35^{1}}a^{5-2}b^{3-2}$$

Subtract 2 from 5.

$$\frac{42^{1}}{35^{1}}a^{3}b^{3-2}$$

Subtract 2 from 3.

$$\frac{42^{1}}{35^{1}}a^{3}b^{1}$$

Reduce the fraction \frac{42}{35} to lowest terms by extracting and canceling out 7.

$$\frac{6}{5}a^{3}b$$

Differentiate w.r.t. a

$$\frac{18ba^{2}}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{42b^{3}}{35b^{2}}a^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{6b}{5}a^{3})$$

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}.

$$3\times \frac{6b}{5}a^{3-1}$$

Do the arithmetic.

$$\frac{18b}{5}a^{2}$$