Solve 125*10^-1*5*1^-2/4^-3*t^-6*5

$$\frac { 125 \times 10 ^ { - 1 } \times 5 \times 1 ^ { - 2 } } { 4 ^ { - 3 } \times t ^ { - 6 } \times 5 }$$

Evaluate

$$800t^{6}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{5\times 25\times 1^{-2}\times \frac{1}{10}}{4^{-3}t^{-6}}$$

Multiply 5 and 25 to get 125.

$$\frac{125\times 1^{-2}\times \frac{1}{10}}{4^{-3}t^{-6}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{125\times 1\times \frac{1}{10}}{4^{-3}t^{-6}}$$

Multiply 125 and 1 to get 125.

$$\frac{125\times \frac{1}{10}}{4^{-3}t^{-6}}$$

Multiply 125 and \frac{1}{10} to get \frac{25}{2}.

$$\frac{\frac{25}{2}}{4^{-3}t^{-6}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{25}{2}}{\frac{1}{64}t^{-6}}$$

Express \frac{\frac{25}{2}}{\frac{1}{64}t^{-6}} as a single fraction.

$$\frac{25}{2\times \frac{1}{64}t^{-6}}$$

Multiply 2 and \frac{1}{64} to get \frac{1}{32}.

$$\frac{25}{\frac{1}{32}t^{-6}}$$

Differentiate w.r.t. t

$$4800t^{5}$$