How do I work this one out? Please

Let's take the first number they gave you: 9^867

If you think about it, this can really be written as (3^2)^867, because the 3^2 would result in 9, and then you would have 9^867.

Let's do this to the second number they gave you too: 9^428 = (3^2)^428

Now we have:

(3^2)^867 x (3^2)^428 x 3^-358 x 3^-2228

Now, we have to remember this rule:

Note that b and c could be any numbers, this just shows you the rule.

This means that (3^2)^867 is really 3^(2*867), which is 3^1734.

Let's do this to the second number too. ⇒ (3^2)^428 = 3^(2*428) = 3^856.

And now we have:

3^1734 x 3^856 x 3^-358 x 3^-2228

Like you said, we can now add up these exponets.

$$\begin{array}{lll}
3^{1734} \times 3^{856} \times 3^{-358} \times 3^{-2228}\\
3^{(1734)+(856)+(-358)+(-2228)}\\
3^{(2590)+(-2586)}\\
3^{2590-2586}\\
3^4\\
3 \times 3 \times 3 \times 3\\
9 \times 9\\
81

\end{array}$$

Ah, you beat me to it CPhill.

Well, looks like we got the same answer, so that's good. :)

9^867 x 9^428 x 3^-358 x 3^-2228

Let's get everything to the same base

Note that 9 = 3²    so we can write...

(3²)⁸⁶⁷ x (3²)⁴²⁸ x (3)^-358 x (3)^-2228    ...and by an exponent law, we have..

3¹⁷³⁴ x 3⁸⁵⁶ x 3^-358 x 3^-2228 

Now, just "keep" the base - (3) - and add/subtract the exponents and that will give you your answer.....!!!

OOPS...sorry ND....I didn't know you were posting on this one, too!!

Well, anyway...yours was a more complete explanation....

I gave both of us points, but I'm thinking about rescinding mine !!!

No that's alright CPhill.

Your answers is plain, simple and to the point.

Mine has a little more information that needed probably. I gave you a point for what it's worth. :)