Solve (8x^3y^2):(4xy)=

$$( 8 x ^ { 3 } y ^ { 2 } ) : ( 4 x y ) =$$

Evaluate

$$2yx^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}x^{3}y^{2}}{4^{1}x^{1}y^{1}}$$

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

$$\frac{8^{1}}{4^{1}}x^{3-1}y^{2-1}$$

Subtract 1 from 3.

$$\frac{8^{1}}{4^{1}}x^{2}y^{2-1}$$

Subtract 1 from 2.

$$\frac{8^{1}}{4^{1}}x^{2}y^{1}$$

Divide 8 by 4.

$$2x^{2}y$$

Differentiate w.r.t. x

$$4xy$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8y^{2}}{4y}x^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2yx^{2})$$

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}.

$$2\times 2yx^{2-1}$$

Do the arithmetic.

$$4yx^{1}$$

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

$$4yx$$