Question

If A^(x) = 3, find A^(10x-x) - 5

Answer 1

\[\huge A^{10x - x} \implies \frac{A^{10x}}{A^x}\]

Answer 2

\[\huge A^{10x - x} - 5 \implies \frac{A^{10x}}{A^x} - 5\]

Answer 3

\[\huge A^{10x} \implies (A^x)^{10}\]

Answer 4

\[\huge \frac{A^{10x}}{A^x} - 5 \implies \frac{(A^x)^{10}}{A^x} - 5\]
does that help?

Answer 5

did you get my point @deehthebee ??

Answer 6

@deehthebee answer him he is asking you something..
Interact with him..

Answer 7

Sorry. First time!

Answer 8

Yes, that was very clear. Thank you so much

Answer 9

so can you do the rest? :)

Answer 10

I'll try to. I'll come back if I need any help

Answer 11

sure ^_^

Answer 12

Sidenote: @lgbasallote Why didn't you just simplify in the beginning (10x-x=9x)?

Answer 13

because the question didnt simplify it :(

Answer 14

i assume they wanna be fancy so i did

Answer 15

i think this is an exponent rule application...so i tried applying

Answer 16

So would it be (A^x)^9 - 5?

Answer 17

yup

Answer 18

Thank you so, so much!

Answer 19

\[\huge \color{maroon}{\mathtt{\text{<tips hat>}}}\]

Answer 20

Sorry I'm back. If A^x = 3, wouldn't the answer be 19678?

Answer 21

wait...ill use me calculator

Answer 22

correct!

Answer 23

Thank you :)

Answer 24

Can someone explain the mathematics behind doing some of these steps though?

Answer 25

which ones?

Answer 26

Just the first one

Answer 27

\[A^{10x-x} \implies \frac{A^{10x}}{A^x}\]
that one?

Answer 28

Yes

Answer 29

Sorry for the delay, the message didn't get through at first

Answer 30

\[\LARGE{(x^{3})(x^{4}) = (x*x*x)*(x*x*x*x) = x^{7}}\]
You add exponents when multiplying similar terms. The other way around also works:
\[\LARGE{x^{7} = (x^{3})(x^{4})}\]
\[\LARGE{x^{7} = x^{6+1} = x^{6}x^{1}}\]
\[\LARGE{x^{7} = x^{8-1} = x^{8}x^{-1}}\]

Negative exponents are another way of saying that you're multiplying by the inverse, so:
\[\LARGE{x^{8}x^{-1} = x^{8}\frac{1}{x^{1}} = \frac{x^{8}}{x^{1}} = \frac{x^{7+1}}{x^{1}}= \frac{x^{7}x^{1}}{x^{1}} = x^{7}}\]

It's just quicker and easier to say 10x-x=9x though :)

Answer 31

Oh ok

Answer 32

Thanks so much!

Answer 33

And knowing is half the battle, GI JOE!!!!!!!!!!

Answer 34

haha nice..that was pretty long @Wired

Answer 35

TY