Let's break down and analyze each part of the given problem step by step:
### Part A - Expression simplification
1. Simplifying [tex]\(\sqrt[25]{3} \)[/tex]:
Expression [tex]\( 25 \sqrt{3} \)[/tex] is already in simplest form. So, no need for further simplification for part D.
### Part B - Expression simplification
2. Simplifying indices and exponents:
Given expression [tex]\( 15^7 \)[/tex]:
Simplifying it by assuming there is a context of same base and exponent:
[tex]\[( 15^7 )\][/tex]
If there are no further instructions or additional context, this expression cannot be simplified further. It is already in its simplest exponential form.
### Part C - Expression simplification
3. Simplifying [tex]\(i 5^5\)[/tex] (an expression involving imaginary unit 'i'):
Let's say [tex]\(i\)[/tex] (imaginary unit) and [tex]\(5^5\)[/tex]:
[tex]\[ i \cdot 5^5 \][/tex]
Since [tex]\(i\)[/tex] represents the imaginary unit, the result stays the same as [tex]\(i \cdot 5^5\)[/tex].
### Part D - Radical simplification
4. Simplifying [tex]\(\sqrt{S^4}\)[/tex]:
Taking roots, we use the property that [tex]\(\sqrt{S^n} = S^{n/2}\)[/tex]:
[tex]\[\sqrt{S^4} = S^{4/2} = S^2\][/tex]
### Part E - Value evaluation
5. Numerical Value 154:
Given [tex]\(154\)[/tex], as a numerical value it stands as it is.
### Final Answer
Given the provided expressions and simplifications, the simplified version stays:
Expression D: 154
The simplified and evaluated step that remains as 154.
