Question

Write 9×9×9×9×9 in exponential form with the base 3

Answer 1

`3^(10)`

Explanation:

Ok, I gotchu. So, basically, you can do this one of two ways: guess until you get it right or solve with algebra. I am gonna show you the algebra way:

First, let's check to see what 9×9×9×9×9 is. It is 59049

9×9×9×9×9 can be rewritten as
`9^(5)` right?

Ok, so now we have to address the main issue here: the problem wants us to give the exponential form but with base 3. To do this, we must find out what power turns 3 into 9. In other words
`3^(x)`=9. "x" in this case is 2 right? because
`3^(2)` is 9.

Alright, so we understand that it takes five 9s multiplied by each other (
`9^(5)`) to reach 59049 and it takes two 3s multiplied by each other (
`3^(2)`) to reach 9. For a visual:

9 x. 9. x. 9. x. 9. x. 9.

is

`3^(2)`. x.
`3^(2)`. x.
`3^(2)`. x.
`3^(2)`. x.
`3^(2)`

So now just evaluate:

`3^(2)`. x.
`3^(2)`. x.
`3^(2)`. x.
`3^(2)`. x.
`3^(2)`

When multiplying exponents that have the same base, you leave the base alone and add the exponents. For example:

`x^(2)` x.
`x^(2)`=
`x^(4)`

So here we just keep our base of 3 and add up all the 2s

so 2+2+2+2+2=10

That leaves us with our answer:
`3^(10)`.

I hope this helps :). Let me know if you need me to explain anything further.