Solve -24x^3y^7/-16y^2x

$$\frac { - 24 x ^ { 3 } y ^ { 7 } } { - 16 y ^ { 2 } x }$$

Evaluate

$$\frac{3x^{2}y^{5}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-24\right)^{1}x^{3}y^{7}}{\left(-16\right)^{1}x^{1}y^{2}}$$

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

$$\frac{\left(-24\right)^{1}}{\left(-16\right)^{1}}x^{3-1}y^{7-2}$$

Subtract 1 from 3.

$$\frac{\left(-24\right)^{1}}{\left(-16\right)^{1}}x^{2}y^{7-2}$$

Subtract 2 from 7.

$$\frac{\left(-24\right)^{1}}{\left(-16\right)^{1}}x^{2}y^{5}$$

Reduce the fraction \frac{-24}{-16} to lowest terms by extracting and canceling out 8.

$$\frac{3}{2}x^{2}y^{5}$$

Differentiate w.r.t. x

$$3xy^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{24y^{7}}{-16y^{2}}\right)x^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y^{5}}{2}x^{2})$$

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}.

$$2\times \frac{3y^{5}}{2}x^{2-1}$$

Do the arithmetic.

$$3y^{5}x^{1}$$

For any term t, t^{1}=t.

$$3y^{5}x$$