Solve (12t^11)(t^4)/8t^-8

$$\frac { ( 12 t ^ { 11 } ) ( t ^ { 4 } ) } { 8 t ^ { - 8 } }$$

Evaluate

$$\frac{3t^{23}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 11 and 4 to get 15.

$$\frac{12t^{15}}{8t^{-8}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3t^{15}}{2t^{-8}}$$

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

$$\frac{3t^{23}}{2}$$

Differentiate w.r.t. t

$$\frac{69t^{22}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{12t^{4}}{8}t^{11-\left(-8\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{3t^{4}}{2}t^{19})$$

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}.

$$19\times \frac{3t^{4}}{2}t^{19-1}$$

Do the arithmetic.

$$\frac{57t^{4}}{2}t^{18}$$