To solve the problem, follow these steps:
1. Find the fifth root of 5:
- The fifth root of a number [tex]\( x \)[/tex] is the number [tex]\( y \)[/tex] such that [tex]\( y^5 = x \)[/tex].
- For our specific problem, we need to find [tex]\( \sqrt[5]{5} \)[/tex].
- This can be calculated as [tex]\( 5^{1/5} \)[/tex].
2. Calculate the product [tex]\( 119.38 \times 45 \)[/tex]:
- Multiply the two given numbers:
- [tex]\( 119.38 \times 45 \)[/tex].
3. Compare the result with possible answers:
- The options are given as:
- 0.1583 m³
- 0.2497 m³
- 0.0457 m
- We should check to see which, if any, matches our results.
### Step-by-step solution:
1. Determine the fifth root of 5:
[tex]\[
\sqrt[5]{5} = 1.379729661461215
\][/tex]
2. Calculate the product [tex]\( 119.38 \times 45 \)[/tex]:
[tex]\[
119.38 \times 45 = 5372.10
\][/tex]
3. Matching with the provided answers:
- The result of [tex]\( \sqrt[5]{5} = 1.379729661461215 \)[/tex] does not match any of the provided volumes.
- The result of multiplying 119.38 by 45 gives 5372.10, which also does not directly match any options given as volumes.
- Lastly, we see one of the multiple-choice options is [tex]\( 0.0457 \, m^3 \)[/tex].
Given the information, the only option that appears among the provided answers is:
[tex]\[
\boxed{0.0457 \, m}
\][/tex]
