Solve 3x^2y^3/27xy^3

$$\frac { 3 x ^ { 2 } y ^ { 3 } } { 27 x y ^ { 3 } }$$

Evaluate

$$\frac{x}{9}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{3^{1}x^{2}y^{3}}{27^{1}x^{1}y^{3}}$$

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

$$\frac{3^{1}}{27^{1}}x^{2-1}y^{3-3}$$

Subtract 1 from 2.

$$\frac{3^{1}}{27^{1}}x^{1}y^{3-3}$$

Subtract 3 from 3.

$$\frac{3^{1}}{27^{1}}xy^{0}$$

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

$$\frac{3^{1}}{27^{1}}x$$

Reduce the fraction \frac{3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{1}{9}x$$

Differentiate w.r.t. x

$$\frac{1}{9} = 0.1111111111111111$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y^{3}}{27y^{3}}x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{9}x^{1})$$

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}.

$$\frac{1}{9}x^{1-1}$$

Do the arithmetic.

$$\frac{1}{9}x^{0}$$

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

$$\frac{1}{9}\times 1$$

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

$$\frac{1}{9}$$