Solve (8x^2y)div(8xy)=

$$( 8 x ^ { 2 } y ) \div ( 8 x y ) =$$

Evaluate

$$x$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 1.

$$8^{0}x^{2-1}y^{1-1}$$

For any number a except 0, a^{0}=1.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$x^{1}y^{0}$$

For any number a except 0, a^{0}=1.

$$8^{0}x$$

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

$$1x$$

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

$$x$$

Differentiate w.r.t. x

$$1$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$x^{1-1}$$

Do the arithmetic.

$$x^{0}$$

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

$$1$$