Exponent question - Why does 4^5+4^5+4^5+4^5 becomes 4*4^5

Why does 4^5+4^5+4^5+4^5 becomes 4*4^5? Is there a rule I should know? Thanks for your help.

Yeah, it's called multiplication:

Let 4^(5) = a

4^5 + 4^5 + 4^5 + 4^5 =>
a + a + a + a =>
4a

So

4a =>
4 * 4^5 =>
4^(5 + 1) =>
4^6

It is called combination by substitution.
Every term in the sum is the same. You could say each of these could be called u, n or any other letter. Make the substitution for each term as 4^5.
u + u + u + u
You can combine these like terms.
4u
You know that u = 4^5. Make that final substitution.
4*4^5
You can simplify in this case, since the number of terms equals the value of the common base.
4^6

Remember the definition of multiplication. a * b means there are a copies of b which are added together. For example, 3 * 2 = 2 + 2 + 2.

Now if you think that 4^5 is something else, it's obvious.

x = 4^5
x + x + x + x = 4x = 4*4^5

This is really easy. Suppose 4⁵ is an apple. How many apples do you have?

                 4⁵ + 4⁵ + 4⁵ + 4⁵

I count four of them. That's right, there are 4-apples. That is, 4 "4⁵"s, or 4*4⁵. That's it! It's that simple!

ciao!
a!ico