Solve -20x^4y^5/-8x^3y^3

$$\frac { - 20 x ^ { 4 } y ^ { 5 } } { - 8 x ^ { 3 } y ^ { 3 } }$$

Evaluate

$$\frac{5xy^{2}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-20\right)^{1}x^{4}y^{5}}{\left(-8\right)^{1}x^{3}y^{3}}$$

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

$$\frac{\left(-20\right)^{1}}{\left(-8\right)^{1}}x^{4-3}y^{5-3}$$

Subtract 3 from 4.

$$\frac{\left(-20\right)^{1}}{\left(-8\right)^{1}}x^{1}y^{5-3}$$

Subtract 3 from 5.

$$\frac{\left(-20\right)^{1}}{\left(-8\right)^{1}}xy^{2}$$

Reduce the fraction \frac{-20}{-8} to lowest terms by extracting and canceling out 4.

$$\frac{5}{2}xy^{2}$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{20y^{5}}{-8y^{3}}\right)x^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{2}}{2}x^{1})$$

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}.

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

Do the arithmetic.

$$\frac{5y^{2}}{2}x^{0}$$

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

$$\frac{5y^{2}}{2}\times 1$$

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

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