Solve 30x^11y^8/6x^6y^4

$$\frac { 30 x ^ { 11 } y ^ { 8 } } { 6 x ^ { 6 } y ^ { 4 } }$$

Evaluate

$$5y^{4}x^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{30^{1}x^{11}y^{8}}{6^{1}x^{6}y^{4}}$$

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

$$\frac{30^{1}}{6^{1}}x^{11-6}y^{8-4}$$

Subtract 6 from 11.

$$\frac{30^{1}}{6^{1}}x^{5}y^{8-4}$$

Subtract 4 from 8.

$$\frac{30^{1}}{6^{1}}x^{5}y^{4}$$

Divide 30 by 6.

$$5x^{5}y^{4}$$

Differentiate w.r.t. x

$$25\left(xy\right)^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{30y^{8}}{6y^{4}}x^{11-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5y^{4}x^{5})$$

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}.

$$5\times 5y^{4}x^{5-1}$$

Do the arithmetic.

$$25y^{4}x^{4}$$