Solve 20x^6y^4/5x^2y

$$\frac { 20 x ^ { 6 } y ^ { 4 } } { 5 x ^ { 2 } y }$$

Evaluate

$$4y^{3}x^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{20^{1}x^{6}y^{4}}{5^{1}x^{2}y^{1}}$$

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

$$\frac{20^{1}}{5^{1}}x^{6-2}y^{4-1}$$

Subtract 2 from 6.

$$\frac{20^{1}}{5^{1}}x^{4}y^{4-1}$$

Subtract 1 from 4.

$$\frac{20^{1}}{5^{1}}x^{4}y^{3}$$

Divide 20 by 5.

$$4x^{4}y^{3}$$

Differentiate w.r.t. x

$$16\left(xy\right)^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20y^{4}}{5y}x^{6-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4y^{3}x^{4})$$

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}.

$$4\times 4y^{3}x^{4-1}$$

Do the arithmetic.

$$16y^{3}x^{3}$$