$$ \rightarrow 4 \cdot 10 ^ { 13 } \cdot 3 \cdot 10 ^ { 11 } \cdot 3 \cdot 10 ^ { - 5 } = $$

Question

UpStudy AI · Accepted Answer

1. Write the expression:
   $$
   4 \cdot 10^{13} \cdot 3 \cdot 10^{11} \cdot 3 \cdot 10^{-5}
   $$

2. Group the numerical factors and the powers of 10:
   $$
   \text{Numerical part: } 4 \cdot 3 \cdot 3
   $$
   $$
   \text{Exponential part: } 10^{13} \cdot 10^{11} \cdot 10^{-5}
   $$

3. Multiply the numerical coefficients:
   $$
   4 \cdot 3 = 12 \quad \text{and} \quad 12 \cdot 3 = 36
   $$

4. Use the exponent rule for multiplication ($$10^a \cdot 10^b = 10^{a+b}$$) on the powers of 10:
   $$
   10^{13} \cdot 10^{11} \cdot 10^{-5} = 10^{13+11-5} = 10^{19}
   $$

5. Combine both parts together:
   $$
   36 \cdot 10^{19}
   $$

6. Express the result in standard scientific notation. Since $$36 = 3.6 \times 10$$, we have:
   $$
   36 \cdot 10^{19} = 3.6 \cdot 10 \cdot 10^{19} = 3.6 \cdot 10^{20}
   $$

Thus, the final result is:
$$
\boxed{3.6 \cdot 10^{20}}
$$
The final result is $$3.6 \times 10^{20}$$.

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