Question

Write 5 to the power of 8 as a quotient of two exponential terms with the same base in four different ways. use negative or zero exponents

Answer 1

So, we are given 5^8. It was happy and content. But then... we had to write it as a quotient of two exponential terms with the same base in four different ways and use negative or zero exponents and ahhhhhh!!!

... anyways...

We'll build a quotient of two exponential terms with the same base 5. Something like this:

5^a / 5^b

We need them to make 5^8 when we are done. I'll first use a zero exponent.

[1] Now, zero exponents are nice since they make things equal 1. Like 5^0 = 1. Well, obviously, 5^8 / 1 = 5^8. So, our first quotient can be:

5^8 / 5^0

Done.

[2] Let's try this on its head. This one's a little weird. Remember that negative exponents flip things upside down. So 5^-8 = 1/5^8    and   1/5^-8 = 5^8 for example. In fact... that's the answer!

5^0 / 5^-8 = 5^8

Done.

[3] Let's try to not use 0s or 8s. We can be clever and do something like this:

5^-1 / 5^-9

What the heck is that? Well, we just flip them and get:

5^-1 / 5^-9 = 5^9 / 5^1 = 5^8

Done.

[4] Can you come up with one last trick on your own? Try it!