Solve 8x^5y^2/2x^4y

$$\frac { 8 x ^ { 5 } y ^ { 2 } } { 2 x ^ { 4 } y }$$

Evaluate

$$4xy$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}x^{5}y^{2}}{2^{1}x^{4}y^{1}}$$

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

$$\frac{8^{1}}{2^{1}}x^{5-4}y^{2-1}$$

Subtract 4 from 5.

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

Subtract 1 from 2.

$$\frac{8^{1}}{2^{1}}xy^{1}$$

Divide 8 by 2.

$$4xy$$

Differentiate w.r.t. x

$$4y$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8y^{2}}{2y}x^{5-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4yx^{1})$$

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}.

$$4yx^{1-1}$$

Do the arithmetic.

$$4yx^{0}$$

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

$$4y\times 1$$

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

$$4y$$