Solve (-15/4x^3y^3)div(-5/24x^2y)

$$( - \frac { 15 } { 4 } x ^ { 3 } y ^ { 3 } ) \div ( - \frac { 5 } { 24 } x ^ { 2 } y )$$

Evaluate

$$18xy^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-\frac{15}{4}\right)^{1}x^{3}y^{3}}{\left(-\frac{5}{24}\right)^{1}x^{2}y^{1}}$$

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

$$\frac{\left(-\frac{15}{4}\right)^{1}}{\left(-\frac{5}{24}\right)^{1}}x^{3-2}y^{3-1}$$

Subtract 2 from 3.

$$\frac{\left(-\frac{15}{4}\right)^{1}}{\left(-\frac{5}{24}\right)^{1}}x^{1}y^{3-1}$$

Subtract 1 from 3.

$$\frac{\left(-\frac{15}{4}\right)^{1}}{\left(-\frac{5}{24}\right)^{1}}xy^{2}$$

Divide -\frac{15}{4} by -\frac{5}{24} by multiplying -\frac{15}{4} by the reciprocal of -\frac{5}{24}.

$$18xy^{2}$$

Differentiate w.r.t. x

$$18y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{\frac{15y^{3}}{4}}{-\frac{5y}{24}}\right)x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18y^{2}x^{1})$$

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}.

$$18y^{2}x^{1-1}$$

Do the arithmetic.

$$18y^{2}x^{0}$$

For any term t except 0, t^{0}=1.

$$18y^{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$18y^{2}$$