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Exponent Problem

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Exponent Problem

by Thonk02 » Fri Jan 30, 2009 1:37 pm
Was doing a practice problem from Manhattan Gmat Number's Properties (Ch. 5) and had a question about distibuting a certain problem.

Manhattan says:

(5X2X2)^N

= 5^N X 2^2N


Shouldnt this be: 5^N X 4^2N (based on the rule that A^2 X B^2 = AB^2)

Is this a mistake?

Bare with me if this looks confusing as this is my first post. [/b]
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by truplayer256 » Fri Jan 30, 2009 1:42 pm
No, Manhattan is correct with their explanation. Here's why:
(5x2x2)^(N)
=(5x4)^(N)
=5^(N) x 4^(N) or 5^(N) x 2^(2N) since 4=2^2
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by DanaJ » Fri Jan 30, 2009 1:45 pm
5X2X2)^N

= 5^N X 2^2N


Shouldnt this be: 5^N X 4^2N (based on the rule that A^2 X B^2 = AB^2)


Here is your mistake: it's not 5^N*4^2N, it's 5^N*4^N, since (5*2*2)^N = (5*4)^N = 5^N*4^N. Anyway, since 2^2 = 4, we can safely say that 4^N = (2^2)^N = 2^2N
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by Thonk02 » Fri Jan 30, 2009 1:51 pm
Thank you both for replying, which i guess leads to one more question to help me clarify this.

I know that if you are multiplying 2 numbers with the same base, you add the exponents (X^A * X^B = X^A+B)

And if multiplying 2 numbers with the same exponents you multiply the bases (A^X * B^X = AB^X)

What happens when you have BOTH the same base and exponents?
(i.e. 2^5 * 2 ^5) shouldn't this technically equal 4^10?? (which isnt right)
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by DanaJ » Fri Jan 30, 2009 1:59 pm
Nope it shouldn't. (2^5)*(2^5) = 2^(5+5) = 2^10. You don't do the two operations at the same time, you settle for the first one. It's like you described it here:

I know that if you are multiplying 2 numbers with the same base, you add the exponents (X^A * X^B = X^A+B)

The only difference is that you just consider A = B.
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by ajmoney09 » Fri Jan 30, 2009 8:43 pm
Thonk02 wrote:Thank you both for replying, which i guess leads to one more question to help me clarify this.

I know that if you are multiplying 2 numbers with the same base, you add the exponents (X^A * X^B = X^A+B)

And if multiplying 2 numbers with the same exponents you multiply the bases (A^X * B^X = AB^X)

What happens when you have BOTH the same base and exponents?
(i.e. 2^5 * 2 ^5) shouldn't this technically equal 4^10?? (which isnt right)
If they are both you settle for one or the other like Dana said....

See if you multiple the bases you get 4^10.....OR if you add the exponents you get 2^10.....now if you do the math they BOTH yield 1024....
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