Solve 2x^9y^2/8x^5y^2

$$\frac { 2 x ^ { 9 } y ^ { 2 } } { 8 x ^ { 5 } y ^ { 2 } }$$

Evaluate

$$\frac{x^{4}}{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}x^{9}y^{2}}{8^{1}x^{5}y^{2}}$$

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

$$\frac{2^{1}}{8^{1}}x^{9-5}y^{2-2}$$

Subtract 5 from 9.

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

Subtract 2 from 2.

$$\frac{2^{1}}{8^{1}}x^{4}y^{0}$$

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

$$\frac{2^{1}}{8^{1}}x^{4}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}x^{4}$$

Differentiate w.r.t. x

$$x^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{2}}{8y^{2}}x^{9-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}x^{4})$$

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}.

$$4\times \frac{1}{4}x^{4-1}$$

Do the arithmetic.

$$x^{3}$$