Solve t^2/t^7

$$\frac { t ^ { 2 } } { t ^ { 7 } }$$

Evaluate

$$\frac{1}{t^{5}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{t^{2}}{t^{7}}$$

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

$$t^{2-7}$$

Subtract 7 from 2.

$$t^{-5}$$

Differentiate w.r.t. t

$$-\frac{5}{t^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{1}t^{2-7})$$

Do the arithmetic.

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

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}.

$$-5t^{-5-1}$$

Do the arithmetic.

$$-5t^{-6}$$