Solve 2x^10y^6/4x^4y^8=

$$\frac { 2 x ^ { 10 } y ^ { 6 } } { 4 x ^ { 4 } y ^ { 8 } } =$$

Evaluate

$$\frac{x^{6}}{2y^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}x^{10}y^{6}}{4^{1}x^{4}y^{8}}$$

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

$$\frac{2^{1}}{4^{1}}x^{10-4}y^{6-8}$$

Subtract 4 from 10.

$$\frac{2^{1}}{4^{1}}x^{6}y^{6-8}$$

Subtract 8 from 6.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x^{6}\times \frac{1}{y^{2}}$$

Differentiate w.r.t. x

$$\frac{3x^{5}}{y^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{6}}{4y^{8}}x^{10-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2y^{2}}x^{6})$$

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}.

$$6\times \frac{1}{2y^{2}}x^{6-1}$$

Do the arithmetic.

$$\frac{3}{y^{2}}x^{5}$$