How to factor out $5^x$ from $5^{x+3}$?

Question

I know this is basic but I am having some confusion here. I need to write $5^x+5^{x+3}$ as $A \times 5^x$. I see on khanacademy and symbolab that I am supposed to factor out $5^x$ as it is a common factor however i don't understand how $5^x$ is a common factor of $5^3$. Any understanding would be appreciated, thanks

Answer 1

Hint: recall that $5^{x+3}=5^x \cdot 5^3$. Can you take it from here?

Answer 2

Using index laws, $$5^{x + 3} = 5^x \cdot 5^3 = 125 \cdot 5^x.$$

Note that this is different from the situation $5^x + 5^3$, where $5^x$ would indeed have to be a factor of $5^3$ in order to (cleanly) take it out as a divisor.

Answer 3

We have

$$5^x+5^{x+3}=5^x+5^x\cdot 5^3=5^x(1+125)=126\cdot 5^x$$