Solve t^5/t^9

$$\frac { t ^ { 5 } } { t ^ { 9 } }$$

Evaluate

$$\frac{1}{t^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{t^{5}}{t^{9}}$$

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

$$t^{5-9}$$

Subtract 9 from 5.

$$t^{-4}$$

Differentiate w.r.t. t

$$-\frac{4}{t^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{1}t^{5-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{-4})$$

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}.

$$-4t^{-4-1}$$

Do the arithmetic.

$$-4t^{-5}$$