TOO MANY TENS

[Eddie Gutia]

Below is a question from MGMAT CAT 2

Q) If n = 10^10 and n^n = 10^d, what is the value of d?

Correct answer is 10^11

My Question: The way the author arrived at this answer is by multiplying 10 * (10 ^ 10). Can you further explain how this multiplication is valid? I think the correct answer should be 10^10^10 which is much higher that 10^11

Thanks,
Aditya

[tim]

We're taking (10^10) to the power of (10^10). If I take a^b to the power of c, then we multiple the exponents to get b*c. That's what's done here. b*c is the equivalent of 10*(10^10), which is the same as (10^1)*(10^10) = 10^11 because we add these exponents.

[Eddie Gutia]

OK, Thanks Tim Sanders

[tim]

You're welcome GUTHEY.ADITYA

[Eddie Gutia]

Tim,

So when you made the statement "If I take a^b to the power of c, then we multiple the exponents to get b*c", what you are saying is 3^3^2 is equivalent to 3 ^ 6 and not 3 ^9. Is that correct?

If yes, is it always true that 3^3^2 is equal to 3^6 or are there any scenarios wherein 3^3^2 equals 3^9. I am confused on how to differentiate the two scenarios. Any help will be appreciated.

Thanks,
Aditya

[RonPurewal]

if it's 3^(3^2), then it's 3^9. (this isn't an exponent rule at all; this is just the result of simplifying 3^2 = 9.)

if it's (3^3)^2, then, per the exponent rule, it's 3^(3•2) = 3^6.

[Eddie Gutia]

Thanks Ron for the response. However, I am referring to the specific scenario where you just see 3^3^2..


Thanks,..

[RonPurewal]

Thanks Ron for the response. However, I am referring to the specific scenario where you just see 3^3^2..


Thanks,..

if i saw just a^b^c (i.e., a regular-size "a", a little "b", and a teeny tiny little "c"), i would probably interpret it as a^(b^c), just because there's no obvious way to simplify a^(b^c).

has that actually happened in an official problem?