Solve x^2*(2y^3)/2x^2y

$$\frac { x ^ { 2 } \times ( 2 y ^ { 3 } ) } { 2 x ^ { 2 } y }$$

Evaluate

$$y^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$2^{1-1}x^{2-2}y^{3-1}$$

Subtract 1 from 1.

$$2^{0}x^{2-2}y^{3-1}$$

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

$$x^{2-2}y^{3-1}$$

Subtract 2 from 2.

$$x^{0}y^{3-1}$$

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

$$y^{3-1}$$

Subtract 1 from 3.

$$x^{0}y^{2}$$

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

$$1y^{2}$$

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

$$y^{2}$$

Differentiate w.r.t. y

$$2y$$

Steps Using Definition of a Derivative

Cancel out 2yx^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{2})$$

The derivative of ax^{n} is nax^{n-1}.

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

Subtract 1 from 2.

$$2y^{1}$$

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

$$2y$$