Question

10 to the second power times 4/10 to the third to the -3rd power times 10 to the -5th power equals what?

Answer 1

To solve the expression \( 10^{2} \times \frac{4}{10^{3}}^{-3} \times 10^{-5} \), we can break it down step by step.

1. **Evaluate \( \frac{4}{10^{3}}^{-3} \)**:
\[
\frac{4}{10^{3}}^{-3} = \left(\frac{4}{10^{3}}\right)^{-3} = \frac{10^{3}}{4^{-3}} = \frac{10^{3}}{\frac{1}{64}} = 10^{3} \cdot 64 = 64 \cdot 10^{3}
\]

2. **Now substitute back into the expression**:
\[
10^{2} \times (64 \cdot 10^{3}) \times 10^{-5}
\]

3. **Reorganize the expression**:
\[
= 64 \cdot 10^{2} \cdot 10^{3} \cdot 10^{-5}
\]

4. **Combine the powers of 10**:
\[
10^{2} \cdot 10^{3} \cdot 10^{-5} = 10^{(2+3-5)} = 10^{0} = 1
\]

5. **Final calculation**:
\[
64 \cdot 10^{0} = 64 \cdot 1 = 64
\]

Therefore, the final answer is:
\[
\boxed{64}
\]