Solve 36x^16y^18/29x^8y^8

$$\frac { 36 x ^ { 16 } y ^ { 18 } } { 29 x ^ { 8 } y ^ { 8 } }$$

Evaluate

$$\frac{36x^{8}y^{10}}{29}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{36^{1}x^{16}y^{18}}{29^{1}x^{8}y^{8}}$$

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

$$\frac{36^{1}}{29^{1}}x^{16-8}y^{18-8}$$

Subtract 8 from 16.

$$\frac{36^{1}}{29^{1}}x^{8}y^{18-8}$$

Subtract 8 from 18.

$$\frac{36^{1}}{29^{1}}x^{8}y^{10}$$

Divide 36 by 29.

$$\frac{36}{29}x^{8}y^{10}$$

Differentiate w.r.t. x

$$\frac{288x^{7}y^{10}}{29}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{36y^{18}}{29y^{8}}x^{16-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{36y^{10}}{29}x^{8})$$

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}.

$$8\times \frac{36y^{10}}{29}x^{8-1}$$

Do the arithmetic.

$$\frac{288y^{10}}{29}x^{7}$$