15m^4^5-3mn+9m^2n^3

To simplify the expression 15m^4^5 - 3mn + 9m^2n^3, let's break it down step by step:

Step 1: Simplify the first term, 15m^4^5.
To simplify this term, we need to understand the exponentiation order. The exponentiation order, also known as the order of operations, states that we need to calculate the exponentiation first, before any other operations.

Since we have an exponentiation operation, let's calculate it:
m^4^5 means raising m to the power of 4, and then raising the result to the power of 5. This can be written as (m^4)^5.

Simplifying (m^4)^5:
(m^4)^5 = m^(4*5) = m^20

So, the first term simplifies to 15m^20.

Step 2: Simplify the second term, -3mn.
As there are no exponents involved here, this term is already in its simplest form.

Step 3: Simplify the third term, 9m^2n^3.
Again, we have exponents in this term, so let's simplify them individually:

9m^2n^3:
m^2 means raising m to the power of 2.
n^3 means raising n to the power of 3.

So, the third term simplifies to 9m^2n^3.

Putting it all together, the simplified expression is:
15m^20 - 3mn + 9m^2n^3