The problem states that a worker bee has a mass of $1 \cdot 10^{-4}$ kg. There are $4 \cdot 10^4$ worker bees living in one hive. We need to find the total mass of all the worker bees in the hive and write the answer in scientific notation.

1. Problem Description

The problem states that a worker bee has a mass of $1 \cdot 10^{-4}$ kg. There are $4 \cdot 10^4$ worker bees living in one hive. We need to find the total mass of all the worker bees in the hive and write the answer in scientific notation.

2. Solution Steps

To find the total mass, we need to multiply the mass of one bee by the number of bees.

So, we have:

Total mass = (mass of one bee) * (number of bees)

Total mass $= (1 \cdot 10^{-4}) \cdot (4 \cdot 10^4)$

Total mass $= (1 \cdot 4) \cdot (10^{-4} \cdot 10^4)$

Using the rule for multiplying exponents with the same base, we have $a^m \cdot a^n = a^{m+n}$.

So, $10^{-4} \cdot 10^4 = 10^{-4+4} = 10^0 = 1$.

Therefore,

Total mass $= 4 \cdot 1 = 4$ kg.

To express 4 in scientific notation, we write it as $4 \cdot 10^0$.

3. Final Answer

$4 \cdot 10^0$