The expression (5 to the power of -1, cubed) times 5 times the square root of 25 times the cube of the square root of 125 simplifies to 125.
Let's simplify the given expression step by step:
Reciprocal of 5: 5 to the power of -1 is the reciprocal of 5, which is 1/5.
Cubing the reciprocal: (1/5)^3 is equal to 1/125.
Multiplying by 5: 1/125 multiplied by 5 is 5/125, which simplifies to 1/25.
Square root of 25: The square root of 25 is 5.
Cubing the square root of 125: The square root of 125 is 5, so cubing it results in 5^3 or 125.
Now, let's put it all together:
(1/25) times 5 times the square root of 25 times the cube of the square root of 125.
This simplifies to (1/25) times 5 times 5 times 125.
This further simplifies to (1 times 5 times 5 times 125) divided by 25.
This gives 3125 divided by 25.
The final simplified value of the given expression is 125.
The question probable may be:
What is the step-by-step simplification process for the expression involving the reciprocal of 5, cubing the reciprocal, multiplying by 5, taking the square root of 25, and cubing the square root of 125, leading to the final result of 125?