Solve -64x^3y^3/-42x^9y^11

$$\frac { - 64 x ^ { 3 } y ^ { 3 } } { - 42 x ^ { 9 } y ^ { 11 } }$$

Evaluate

$$\frac{32}{21x^{6}y^{8}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-64\right)^{1}x^{3}y^{3}}{\left(-42\right)^{1}x^{9}y^{11}}$$

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

$$\frac{\left(-64\right)^{1}}{\left(-42\right)^{1}}x^{3-9}y^{3-11}$$

Subtract 9 from 3.

$$\frac{\left(-64\right)^{1}}{\left(-42\right)^{1}}x^{-6}y^{3-11}$$

Subtract 11 from 3.

$$\frac{\left(-64\right)^{1}}{\left(-42\right)^{1}}\times \frac{1}{x^{6}}y^{-8}$$

Reduce the fraction \frac{-64}{-42} to lowest terms by extracting and canceling out 2.

$$\frac{32}{21}\times \frac{1}{x^{6}}\times \frac{1}{y^{8}}$$

Differentiate w.r.t. x

$$-\frac{64}{7x^{7}y^{8}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{64y^{3}}{-42y^{11}}\right)x^{3-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32}{21y^{8}}x^{-6})$$

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}.

$$-6\times \frac{32}{21y^{8}}x^{-6-1}$$

Do the arithmetic.

$$\left(-\frac{64}{7y^{8}}\right)x^{-7}$$