Solve x^20/x^160

$$\frac { x ^ { 20 } } { x ^ { 160 } }$$

Evaluate

$$\frac{1}{x^{140}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{20}}{x^{160}}$$

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

$$x^{20-160}$$

Subtract 160 from 20.

$$x^{-140}$$

Differentiate w.r.t. x

$$-\frac{140}{x^{141}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{20-160})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-140})$$

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}.

$$-140x^{-140-1}$$

Do the arithmetic.

$$-140x^{-141}$$