Answer:
There are many ways we can write [tex]5^{11}[/tex] one of them being that we just write 11 fives being multiplied against each other like the following:
[tex]5*5*5*5*5*5*5*5*5*5*5[/tex]
This can seem very repetitive which is why powers are a lot more helpful. We can also rewrite [tex]5^{11}[/tex] using the power in the bottom of a fraction. The way that we do this is put [tex]5^{-11}[/tex] on the bottom which can then be flipped to the top with a positive power and will be the same.
[tex]\frac{1}{5^{-11}}[/tex]
The final way that we can rewrite [tex]5^{11}[/tex] is by using several different powers. We can do [tex]5^6*5^5[/tex] which will equal the same thing as [tex]5^{11}[/tex] because the base is the same and what we basically do is just add up the powers together to get back to 11.
[tex]5^6*5^5[/tex]
