Solve (-27x^2y)div(-9xy)=

$$( - 27 x ^ { 2 } y ) \div ( - 9 x y ) =$$

Evaluate

$$3x$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-27\right)^{1}x^{2}y^{1}}{\left(-9\right)^{1}x^{1}y^{1}}$$

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

$$\frac{\left(-27\right)^{1}}{\left(-9\right)^{1}}x^{2-1}y^{1-1}$$

Subtract 1 from 2.

$$\frac{\left(-27\right)^{1}}{\left(-9\right)^{1}}x^{1}y^{1-1}$$

Subtract 1 from 1.

$$\frac{\left(-27\right)^{1}}{\left(-9\right)^{1}}xy^{0}$$

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

$$\frac{\left(-27\right)^{1}}{\left(-9\right)^{1}}x$$

Divide -27 by -9.

$$3x$$

Differentiate w.r.t. x

$$3$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{27y}{-9y}\right)x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})$$

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}.

$$3x^{1-1}$$

Do the arithmetic.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$