Solve q^9/-8*q^-3

$$\frac { q ^ { 9 } } { - 8 \cdot q ^ { - 3 } }$$

Evaluate

$$-\frac{q^{12}}{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(q^{1}\right)^{9}\times \frac{1}{-8q^{-3}}$$

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

$$1^{9}\left(q^{1}\right)^{9}\times \frac{1}{-8}\times \frac{1}{q^{-3}}$$

Use the Commutative Property of Multiplication.

$$1^{9}\times \frac{1}{-8}\left(q^{1}\right)^{9}\times \frac{1}{q^{-3}}$$

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

$$1^{9}\times \frac{1}{-8}q^{9}q^{-3\left(-1\right)}$$

Multiply -3 times -1.

$$1^{9}\times \frac{1}{-8}q^{9}q^{3}$$

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

$$1^{9}\times \frac{1}{-8}q^{9+3}$$

Add the exponents 9 and 3.

$$1^{9}\times \frac{1}{-8}q^{12}$$

Raise -8 to the power -1.

$$-\frac{1}{8}q^{12}$$

Differentiate w.r.t. q

$$-\frac{3q^{11}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{1}{-8}q^{9-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(-\frac{1}{8}q^{12})$$

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}.

$$12\left(-\frac{1}{8}\right)q^{12-1}$$

Do the arithmetic.

$$-\frac{3}{2}q^{11}$$