# How to add numbers with same base but unknown exponents?

I'm taking a university math course despite knowing better. Among the straightforward problems I encountered the following:

Simplify:

$$5^x +5^{x+2}$$

The answer is supposed to be $$26*5^x$$

How am I supposed to arrive at this conclusion, do I interpret this as some kind of short geometric sum?

$$5^{x}+5^{x+2}=5^{x}+5^{x}\cdot 5^{2}=5^{x}(1+5^{2})=5^{x}\cdot 26$$
• I didn't understand that last step, why can $5^x(1+5^2)$ be written as $5^x*26$? – Magnus Jan 22 '19 at 17:22
• Because $5^2=25$ – Rhys Hughes Jan 22 '19 at 17:23