Question

3 different ways to write 5^11

Answer 1

Answer:

There are many ways we can write $5^{11}$ one of them being that we just write 11 fives being multiplied against each other like the following:

$5*5*5*5*5*5*5*5*5*5*5$

This can seem very repetitive which is why powers are a lot more helpful.  We can also rewrite $5^{11}$ using the power in the bottom of a fraction.  The way that we do this is put $5^{-11}$ on the bottom which can then be flipped to the top with a positive power and will be the same.

$\frac{1}{5^{-11}}$

The final way that we can rewrite $5^{11}$ is by using several different powers.  We can do $5^6*5^5$ which will equal the same thing as $5^{11}$ because the base is the same and what we basically do is just add up the powers together to get back to 11.

$5^6*5^5$