Exponents : Find no of zeros

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After solving I got 5^32 3^8 2^32
After this what needs to be done

As 5 x 2 = 10 (1 zero)

Now if we have 5 ^2 and 2^ 2 = 100 (on multiplying)
So you can say if power is same, then that is equal to number of zeroes.

If the case is different, for example - 5^3 and 2^4 => we take least number => so, number of zeroes = 3

I didnt follow why u took 5 x 2 = 10

The question asks for number of zeros left to its decimal point.
That simply means how many zeroes one can have.

SO, now lets take example

250 - 25 * 10 = 5^2 and 2 x 5 = 5^3 and 2^1

Here you can see we combine factors of 10.

another example -
4300
here you can say 4300 = 43 x 100 = 43 x 10 x 10 = 43 x 2^2 x 5^2

SO, this basically means how many 10s can you create from the question asked.

According to question,
we have 125^14 x 48^ 8 => 2^32 x 3^8 x 5^42

here we can see power of 2 and 5 are different, and therefore we take smaller one i.e., 32.

So answer should be 32

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Oh so here we consider the factors that make 10 and take the factors with the least no
Do u have another example so I cud a better clarity in this

Lets leave this for a moment,
let me ask how do you know how many zeroes will this number have 35 * 80 ?

Also, mention you thoughts on how you proceed with this?

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So for 35 * 80
35 β†’ 7 x 5
80 β†’ 2^4 x 5
Final : 7^1 5^2 2^4

5x2 makes up 10 so then between 5 and 2 I take the power with the least value
In this case its 2 (5^2)

Yes, it’s correct.

Was this helpful?
if you need more help, I don’t have examples but if you can find some then I can definitely help.

Thank you so much. Now I realize that solving these sums is really fun :smiley:
Thanks for this method Thank you once again

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