Problem Solving

I'm a little confuse can anyone explain me why

2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2^6 + 3^6 and not 13^5?

Thank you.

2^5 + 2^5 + 3^5 + 3^5 + 3^5 = ( 2^5 + 2^5 ) + ( 3^5 + 3^5 + 3^5 ) =
2 * 2^5 + 3 * 3^5 = 2^(5+1) + 3 ^ (5+1)

Thanks. Is there a rule I should know when adding numbers of different base and same exponent?

msquare wrote:Thanks. Is there a rule I should know when adding numbers of different base and same exponent?

Nope.
Good reference: https://www.jug.net/wt/exponentrules.gif

Ok, this is tricky because it makes yuo want to use yuor exponent rules and ignore the fact that the question is about adding exponents (and remember yuo can't combine exponents when adding/subtracting).

My easy way to deal with this is to think: how many of each exponent do I have?

2 x 2^5
3 x 3^5

I set this up as 2^1 (2^5) + 3^1(3^5)

because the bases are the same you add the exponents and keep the base, so the anszer is 2^6 + 3^6.

Hope this helps!