Solve 2q^8/q^9

$$\frac { 2 q ^ { 8 } } { q ^ { 9 } }$$

Evaluate

$$\frac{2}{q}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2q^{8}\right)^{1}\times \frac{1}{q^{9}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$2^{1}\left(q^{8}\right)^{1}\times \frac{1}{1}\times \frac{1}{q^{9}}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times \frac{1}{1}\left(q^{8}\right)^{1}\times \frac{1}{q^{9}}$$

To raise a power to another power, multiply the exponents.

$$2^{1}\times \frac{1}{1}q^{8}q^{9\left(-1\right)}$$

Multiply 9 times -1.

$$2^{1}\times \frac{1}{1}q^{8}q^{-9}$$

To multiply powers of the same base, add their exponents.

$$2^{1}\times \frac{1}{1}q^{8-9}$$

Add the exponents 8 and -9.

$$2^{1}\times \frac{1}{1}\times \frac{1}{q}$$

Raise 2 to the power 1.

$$2\times \frac{1}{1}\times \frac{1}{q}$$

Differentiate w.r.t. q

$$-\frac{2}{q^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{2}{1}q^{8-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(2\times \frac{1}{q})$$

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}.

$$-2q^{-1-1}$$

Do the arithmetic.

$$-2q^{-2}$$