Solve 9x^2/x^14=

$$\frac { 9 x ^ { 2 } } { x ^ { 14 } } =$$

Evaluate

$$\frac{9}{x^{12}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(9x^{2}\right)^{1}\times \frac{1}{x^{14}}$$

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

$$9^{1}\left(x^{2}\right)^{1}\times \frac{1}{1}\times \frac{1}{x^{14}}$$

Use the Commutative Property of Multiplication.

$$9^{1}\times \frac{1}{1}\left(x^{2}\right)^{1}\times \frac{1}{x^{14}}$$

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

$$9^{1}\times \frac{1}{1}x^{2}x^{14\left(-1\right)}$$

Multiply 14 times -1.

$$9^{1}\times \frac{1}{1}x^{2}x^{-14}$$

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

$$9^{1}\times \frac{1}{1}x^{2-14}$$

Add the exponents 2 and -14.

$$9^{1}\times \frac{1}{1}x^{-12}$$

Raise 9 to the power 1.

$$9\times \frac{1}{1}x^{-12}$$

Differentiate w.r.t. x

$$-\frac{108}{x^{13}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{1}x^{2-14})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{-12})$$

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}.

$$-12\times 9x^{-12-1}$$

Do the arithmetic.

$$-108x^{-13}$$