Solve t^2/t^9

$$\frac { t ^ { 2 } } { t ^ { 9 } }$$

Evaluate

$$\frac{1}{t^{7}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{t^{2}}{t^{9}}$$

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

$$t^{2-9}$$

Subtract 9 from 2.

$$t^{-7}$$

Differentiate w.r.t. t

$$-\frac{7}{t^{8}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{-7})$$

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}.

$$-7t^{-7-1}$$

Do the arithmetic.

$$-7t^{-8}$$