A Nice Olympiad Exponential Multiplication Problem #short #olympiad #mathematics #maths #exponents

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[nishantsaini_]

I think question is more simplified than the answer😅

[Zindagijhand]

If this is olympiad question then I am mathematician😜.

[Lilynaranus]

I'm a biology student, but I love studying math too.

[Cyrus_mitra.]

in our language it is called basic maths 😂

[nbooth]

The original form is simpler to me. And prime factorized.

[_Divyanshu_Raj]

I studied this when I was in class 7th😅😂

[johnyoung]

I got that much in my head. But when I decided to use binomial theorem on (100+8)^11 I had to use paper.

[XYZ_______________]

Le science students:-taking log on both sides😂😂

[editormeltstar]

first i thought it is easy then i thought it is hard then i thought it is easy thanks sir

[motivatemind_k]

Log(2^22×3^33)=logx

Log(2^22)+log(3^33)=logx

22log2 + 33log3= logx

22(0.3)+33(0.48) = logx

22.44=logx


x=10^22.44

Simplified answer is 108^11
Log(108^11)=log(y)
11log108 =log(y)
Log108 approx 2.04
So log(y)= 22.44
y=10^22.44

x=y, so the answer of this question is approx 10^22

[cpklapper]

108^11 = (100+8)^11
which can be reduced further using binomial expansion. The notational set is too limited here to set out that expansion, but you will recollect that the coefficients start with
(1 2 1)
(1 3 3 1) and then
(1 4 6 4 1) and so on up to
(1 11 55 165 … 165 55 11 1)
with corresponding exponents for 100 and 8.
The whole exercise is more easily worked out on paper than on a texting keyboard.

[xorbe]

This was really easy to do mentally in a few seconds.

[msecke]

2^22 x 3^33 = 3^11 x 6^22. 3^11 = 3^5 x 3^5 x 3 = 243 x 243 x 3. 243 = 216 + 24 + 3 = 1 x 6^3 + 0 x 6^2 + 4 x 6^1 + 3 x 6^0, so 243 decimal is 1043 hexal. Therefore 3^11 decimal is 1043 x 1043 x 3 hexal which is 3444043 hexal, so the end result in hexal is 34, 440, 430, 000, 000, 000, 000, 000, 000, 000

[EnginAtik]

2^22*3^33 is the prime factorized form and and it is the simplest form already.

[aumoelwal]

I wouldn't have solved it without knowing this 😯😮

[Blue]

We need to know what kind of 'simplify' that question is requiring

Like:
Express this to the form of a^b (When a, b ∈ N)

[SonicRicky]

I guess we all need to come to a consensus on what it means for something to be simplified

[funnyfish]

Great explanation. I understood everything.

[srishtisharma]

To all the people making fun of the Question difficulty level, why didn't you clear Olympiad or JEE exam then ??? That says a lot about your mental level overall !!!

[UberHummus]

Simplifying is very easy. Solving takes a bit more time.

I just use Vedic method of arrow and cross