How to add numbers with same base but unknown exponents?

Question

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?

pwerth · Accepted Answer · 2019-01-22 17:19:05Z

9

$5^{x}+5^{x+2}=5^{x}+5^{x}\cdot 5^{2}=5^{x}(1+5^{2})=5^{x}\cdot 26$

answered Jan 22, 2019 at 17:19

pwerth

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$\begingroup$ I didn't understand that last step, why can $5^x(1+5^2) $ be written as $5^x*26$? $\endgroup$
– Magnus
Jan 22, 2019 at 17:22
5

$\begingroup$ Because $5^2=25$ $\endgroup$
– Rhys Hughes
Jan 22, 2019 at 17:23
$\begingroup$ ahh allright I guess I'm just tired today. $\endgroup$
– Magnus
Jan 22, 2019 at 17:24

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