Solve -x^130/x^216

$$\frac { - x ^ { 130 } } { x ^ { 216 } }$$

Evaluate

$$-\frac{1}{x^{86}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-x^{130}\right)^{1}\times \frac{1}{x^{216}}$$

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

$$-\left(x^{130}\right)^{1}\times \frac{1}{1}\times \frac{1}{x^{216}}$$

Use the Commutative Property of Multiplication.

$$-\frac{1}{1}\left(x^{130}\right)^{1}\times \frac{1}{x^{216}}$$

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

$$-\frac{1}{1}x^{130}x^{216\left(-1\right)}$$

Multiply 216 times -1.

$$-\frac{1}{1}x^{130}x^{-216}$$

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

$$-\frac{1}{1}x^{130-216}$$

Add the exponents 130 and -216.

$$-\frac{1}{1}x^{-86}$$

Differentiate w.r.t. x

$$\frac{86}{x^{87}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{1}{1}\right)x^{130-216})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{-86})$$

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}.

$$-86\left(-1\right)x^{-86-1}$$

Do the arithmetic.

$$86x^{-87}$$