Solve 6x^8y^9/3x^2y^3

$$\frac { 6 x ^ { 8 } y ^ { 9 } } { 3 x ^ { 2 } y ^ { 3 } }$$

Evaluate

$$2\left(xy\right)^{6}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{8}y^{9}}{3^{1}x^{2}y^{3}}$$

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

$$\frac{6^{1}}{3^{1}}x^{8-2}y^{9-3}$$

Subtract 2 from 8.

$$\frac{6^{1}}{3^{1}}x^{6}y^{9-3}$$

Subtract 3 from 9.

$$\frac{6^{1}}{3^{1}}x^{6}y^{6}$$

Divide 6 by 3.

$$2x^{6}y^{6}$$

Differentiate w.r.t. x

$$12x^{5}y^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{9}}{3y^{3}}x^{8-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2y^{6}x^{6})$$

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}.

$$6\times 2y^{6}x^{6-1}$$

Do the arithmetic.

$$12y^{6}x^{5}$$