Solve 8x^6y^3/40xy^6

$$\frac { 8 x ^ { 6 } y ^ { 3 } } { 40 x y ^ { 6 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}x^{6}y^{3}}{40^{1}x^{1}y^{6}}$$

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

$$\frac{8^{1}}{40^{1}}x^{6-1}y^{3-6}$$

Subtract 1 from 6.

$$\frac{8^{1}}{40^{1}}x^{5}y^{3-6}$$

Subtract 6 from 3.

$$\frac{8^{1}}{40^{1}}x^{5}y^{-3}$$

Reduce the fraction \frac{8}{40} to lowest terms by extracting and canceling out 8.

$$\frac{1}{5}x^{5}\times \frac{1}{y^{3}}$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8y^{3}}{40y^{6}}x^{6-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{5y^{3}}x^{5})$$

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}.

$$5\times \frac{1}{5y^{3}}x^{5-1}$$

Do the arithmetic.

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