Simplify

3*3 to the power root 40 - 4* 3 to the power root 320 - 5 to the power root 5?

did you mean

3^3 √40 - 4^3 √320 - 5√5 ????

To simplify the given expression involving roots and exponents, we will follow these steps:

Step 1: Simplify the roots to their numerical values.
Step 2: Evaluate the exponents.
Step 3: Perform the multiplications and subtractions.

Let's break it down:

Step 1: Simplify the roots.
The square root (√) of 40 can be expressed as 2√10 because 10 is the largest perfect square that divides 40.
Similarly, the square root of 320 can be written as 8√5 since 5 is the largest perfect square that divides 320.
The fifth root (∛) of 5 remains as ∛5, as there are no perfect powers of 5 that divide 5.

Step 2: Evaluate the exponents.
3 to the power of √40 is equal to 3^(2√10).
4 multiplied by 3 to the power of √320 is equal to 4 * 3^(8√5).
5 to the power of ∛5 is equal to 5^(∛5).

Step 3: Perform the multiplications and subtractions.
The simplified expression becomes:
3^(2√10) - 4 * 3^(8√5) - 5^(∛5)

And that's the final simplified form of the expression.

sounds more like

3*3^√40 - 4*3^√320 - 5^√5

Not much for simplification. I think it's more likely

3*√40 - 4*√320 - 5√5
3*√4√10 - 4*√64√5 - 5√5
12√10 - 32√5 - 5√5
12√10 - 37√5
(12√2-37)√5

But that's just a guess.