Solve 34x^10y^8/2x^8y^6

$$\frac { 34 x ^ { 10 } y ^ { 8 } } { 2 x ^ { 8 } y ^ { 6 } }$$

Evaluate

$$17\left(xy\right)^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{34^{1}x^{10}y^{8}}{2^{1}x^{8}y^{6}}$$

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

$$\frac{34^{1}}{2^{1}}x^{10-8}y^{8-6}$$

Subtract 8 from 10.

$$\frac{34^{1}}{2^{1}}x^{2}y^{8-6}$$

Subtract 6 from 8.

$$\frac{34^{1}}{2^{1}}x^{2}y^{2}$$

Divide 34 by 2.

$$17x^{2}y^{2}$$

Differentiate w.r.t. x

$$34xy^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{34y^{8}}{2y^{6}}x^{10-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(17y^{2}x^{2})$$

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}.

$$2\times 17y^{2}x^{2-1}$$

Do the arithmetic.

$$34y^{2}x^{1}$$

For any term t, t^{1}=t.

$$34y^{2}x$$