Solve 10q^4r^6/2q^2r^2

$$\frac { 10 q ^ { 4 } r ^ { 6 } } { 2 q ^ { 2 } r ^ { 2 } }$$

Evaluate

$$5q^{2}r^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}q^{4}r^{6}}{2^{1}q^{2}r^{2}}$$

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

$$\frac{10^{1}}{2^{1}}q^{4-2}r^{6-2}$$

Subtract 2 from 4.

$$\frac{10^{1}}{2^{1}}q^{2}r^{6-2}$$

Subtract 2 from 6.

$$\frac{10^{1}}{2^{1}}q^{2}r^{4}$$

Divide 10 by 2.

$$5q^{2}r^{4}$$

Differentiate w.r.t. q

$$10qr^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{10r^{6}}{2r^{2}}q^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(5r^{4}q^{2})$$

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}.

$$2\times 5r^{4}q^{2-1}$$

Do the arithmetic.

$$10r^{4}q^{1}$$

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

$$10r^{4}q$$