Solve 12x^8y^5/8x^3y^4

$$\frac { 12 x ^ { 8 } y ^ { 5 } } { 8 x ^ { 3 } y ^ { 4 } }$$

Evaluate

$$\frac{3yx^{5}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}x^{8}y^{5}}{8^{1}x^{3}y^{4}}$$

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

$$\frac{12^{1}}{8^{1}}x^{8-3}y^{5-4}$$

Subtract 3 from 8.

$$\frac{12^{1}}{8^{1}}x^{5}y^{5-4}$$

Subtract 4 from 5.

$$\frac{12^{1}}{8^{1}}x^{5}y^{1}$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

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

Differentiate w.r.t. x

$$\frac{15yx^{4}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12y^{5}}{8y^{4}}x^{8-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y}{2}x^{5})$$

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}.

$$5\times \frac{3y}{2}x^{5-1}$$

Do the arithmetic.

$$\frac{15y}{2}x^{4}$$