Solve t^9divt^3

$$t ^ { 9 } \div t ^ { 3 }$$

Evaluate

$$t^{6}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{t^{9}}{t^{3}}$$

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

$$t^{9-3}$$

Subtract 3 from 9.

$$t^{6}$$

Differentiate w.r.t. t

$$6t^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{1}t^{9-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{6})$$

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}.

$$6t^{6-1}$$

Do the arithmetic.

$$6t^{5}$$