Solve 90a^14b^14/15a^4b^3

$$\frac { 90 a ^ { 14 } b ^ { 14 } } { 15 a ^ { 4 } b ^ { 3 } }$$

Evaluate

$$6a^{10}b^{11}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{90^{1}a^{14}b^{14}}{15^{1}a^{4}b^{3}}$$

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

$$\frac{90^{1}}{15^{1}}a^{14-4}b^{14-3}$$

Subtract 4 from 14.

$$\frac{90^{1}}{15^{1}}a^{10}b^{14-3}$$

Subtract 3 from 14.

$$\frac{90^{1}}{15^{1}}a^{10}b^{11}$$

Divide 90 by 15.

$$6a^{10}b^{11}$$

Differentiate w.r.t. a

$$60a^{9}b^{11}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{90b^{14}}{15b^{3}}a^{14-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6b^{11}a^{10})$$

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}.

$$10\times 6b^{11}a^{10-1}$$

Do the arithmetic.

$$60b^{11}a^{9}$$