what is 5 on the square root of 2m divied by 5 on the square root of 3m cubed

To simplify the expression (5√2m) / (5√3m³), we can follow these steps:

Step 1: Simplify the numerator: 5√2m
- Since both terms have the same base (√2), we can combine them by multiplying their coefficients:
5 * √2 = 5√2
- The term "m" remains unchanged.

Step 2: Simplify the denominator: 5√3m³
- Again, both terms have the same base (√3), so we can combine them:
5 * √3 = 5√3
- To simplify m³, we can rewrite it as m * m * m.
The square root of m is √m, so the cube root of m³ is ∛(m * m * m) = ∛m³ = m.
- Therefore, the denominator becomes: 5√3m.

Now, let's put the simplified numerator and denominator together:
(5√2m) / (5√3m)

Since the numerator and denominator are identical, we can cancel them out, resulting in: 1.

So, the answer to the expression (5√2m) / (5√3m³) is 1.