Solve 36a^7b^3/9a^3b^2

$$\frac { 36 a ^ { 7 } b ^ { 3 } } { 9 a ^ { 3 } b ^ { 2 } }$$

Evaluate

$$4ba^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{36^{1}a^{7}b^{3}}{9^{1}a^{3}b^{2}}$$

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

$$\frac{36^{1}}{9^{1}}a^{7-3}b^{3-2}$$

Subtract 3 from 7.

$$\frac{36^{1}}{9^{1}}a^{4}b^{3-2}$$

Subtract 2 from 3.

$$\frac{36^{1}}{9^{1}}a^{4}b^{1}$$

Divide 36 by 9.

$$4a^{4}b$$

Differentiate w.r.t. a

$$16ba^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{36b^{3}}{9b^{2}}a^{7-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4ba^{4})$$

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}.

$$4\times 4ba^{4-1}$$

Do the arithmetic.

$$16ba^{3}$$