Exponents

[cschramke]

If you have more than one exponent with the same exponent number but different bases, is it possible to combine these to be more simple? ie: (9^x)(7^x)? In some cases you can multiply the base and keep "x" as the exponent but this doesn't seem to always be the case.. maybe I am over thinking it. Please advise.

[RonPurewal]

If you have more than one exponent with the same exponent number but different bases, is it possible to combine these to be more simple? ie: (9^x)(7^x)? In some cases you can multiply the base and keep "x" as the exponent but this doesn't seem to always be the case.. maybe I am over thinking it. Please advise.

Ya, you can always do that. So that's 63^x.

You can generally figure out whether a rule is real by just writing out the expressions and watching what happens.
For instance, try x = 6 (for no particular reason) in the problem above.
then that's (9^6)(7^6)
which is 9x9x9x9x9x9 x 7x7x7x7x7x7
which is (9x7)(9x7)(9x7)(9x7)(9x7)(9x7)
which is 63^6.
You should probably see the general pattern at work right there. If you don't, throw in another number or two until you're convinced.

[BlasP747]

First of all sorry for rescuing such an old post,

I'm going again though M's Algebra book and I've realised that on page 63 it states that (4^(y+1))*(3^(y+1)) = (4*3)^(y+1) = 12^(y+1)

Now, the question is, since we've always learnt that exponents are to be combined (following the common combination rules) only when they have the same base, can I understand that, even though it is not mentioned in the book (or at least I couldn't find it) when they have different bases but the same exponent, they can also be combined following the classical rules?

Thank you very much for your help,

B

[Sage Pearce-Higgins]

I'm not sure that I fully understand your question about 'classical rules'. There are a number of rules for manipulating exponents described in chapter 4 of the Algebra Strategy Guide. Learning to apply these rules and develop a flexibility for working with exponents is the goal here.

The problem that you're referring to relies on the rule concerning "A compound base" on page 56. What makes it tricky is that it uses the rule in reverse. It's easy to see that, for example, (3*5)^2 is (3^2)*(5^2), but we can equally reverse the situation and say that (3^2)*(5^2) is (3*5)^2.