Question

Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?
1
2
8
10

Answer 1

To solve the expression \(\left(\frac{10^4 \cdot 5^2}{10^3 \cdot 5^3}\right)^3\), we will simplify it step by step before cubing it.

1. **Simplify the fraction**:

\[
\frac{10^4 \cdot 5^2}{10^3 \cdot 5^3}
\]

We can split this into two parts:

- For the \(10\) terms:
\[
\frac{10^4}{10^3} = 10^{4-3} = 10^1 = 10
\]

- For the \(5\) terms:
\[
\frac{5^2}{5^3} = 5^{2-3} = 5^{-1} = \frac{1}{5}
\]

Therefore, the entire fraction simplifies to:
\[
10 \cdot \frac{1}{5} = \frac{10}{5} = 2
\]

2. **Cube the result**:

Now we take the result from the simplification (which is \(2\)) and cube it:
\[
2^3 = 8
\]

Thus, the value of the original expression \(\left(\frac{10^4 \cdot 5^2}{10^3 \cdot 5^3}\right)^3\) is \(\boxed{8}\).