Solve 60x^4y^2/10x^3y=

$$\frac { 60 x ^ { 4 } y ^ { 2 } } { 10 x ^ { 3 } y } =$$

Evaluate

$$6xy$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{60^{1}x^{4}y^{2}}{10^{1}x^{3}y^{1}}$$

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

$$\frac{60^{1}}{10^{1}}x^{4-3}y^{2-1}$$

Subtract 3 from 4.

$$\frac{60^{1}}{10^{1}}x^{1}y^{2-1}$$

Subtract 1 from 2.

$$\frac{60^{1}}{10^{1}}xy^{1}$$

Divide 60 by 10.

$$6xy$$

Differentiate w.r.t. x

$$6y$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{60y^{2}}{10y}x^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6yx^{1})$$

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}.

$$6yx^{1-1}$$

Do the arithmetic.

$$6yx^{0}$$

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

$$6y\times 1$$

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

$$6y$$