Solve (5x^12y^2/10xy^9)

$$( \frac { 5 x ^ { 12 } y ^ { 2 } } { 10 x y ^ { 9 } } )$$

Evaluate

$$\frac{x^{11}}{2y^{7}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{5^{1}x^{12}y^{2}}{10^{1}x^{1}y^{9}}$$

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

$$\frac{5^{1}}{10^{1}}x^{12-1}y^{2-9}$$

Subtract 1 from 12.

$$\frac{5^{1}}{10^{1}}x^{11}y^{2-9}$$

Subtract 9 from 2.

$$\frac{5^{1}}{10^{1}}x^{11}y^{-7}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}x^{11}\times \frac{1}{y^{7}}$$

Differentiate w.r.t. x

$$\frac{11x^{10}}{2y^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{2}}{10y^{9}}x^{12-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2y^{7}}x^{11})$$

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}.

$$11\times \frac{1}{2y^{7}}x^{11-1}$$

Do the arithmetic.

$$\frac{11}{2y^{7}}x^{10}$$