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Bunuel
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If (125^14)(48^8) is written out as an integer, how many consecutive 25 Mar 2021, 09:00
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C
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67% (01:29) correct 33% (01:46) wrong based on 191 sessions

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If \((125^{14})(48^8)\) is written out as an integer, how many consecutive zeroes will that integer have at the end?

A. 8
B. 14
C. 32
D. 42
E. 74
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C
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If (125^14)(48^8) is written out as an integer, how many consecutive 25 Mar 2021, 09:02
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Bunuel
If \((125^{14})(48^8)\) is written out as an integer, how many consecutive zeroes will that integer have at the end?

A. 8
B. 14
C. 32
D. 42
E. 74
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We want to know how many powers of 10s we can find. 10 = 2*5 so find all the 2's and 5's.

\(125^{14}*48^8 = (5^3)^{14}*(3*2^4)^8 = 5^{42}*3^8*2^{32}\). Then we can only find 32 multiples of ten from 42 fives and 32 twos.

Ans: C
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If (125^14)(48^8) is written out as an integer, how many consecutive 25 Mar 2021, 09:07
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Asked: If \((125^{14})(48^8)\) is written out as an integer, how many consecutive zeroes will that integer have at the end?

\((125^{14})(48^8) = 5^{42}*16^8*3^8 = 5^{42}2^{32}3^8\)

It will have 32 zeros at the end since there are 32 2s and 42 5s resulting in 32 10s.

IMO C
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If (125^14)(48^8) is written out as an integer, how many consecutive 14 Jun 2021, 11:43
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Is this math from the "Number System" chapter?
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If (125^14)(48^8) is written out as an integer, how many consecutive 28 Dec 2023, 04:14
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If \((125^{14})(48^8)\) is written out as an integer, how many consecutive zeroes will that integer have at the end?

To find the number of consecutive numbers we need to find what is the power of 10 in the given number.
And to find the power of 10 we need to find out how many 5's and 2's are there which can get multiplied to give us 10

\(125^{14}*48^8\)
125 can be written as \(5^3\)
=> \((5^3)^{14}*48^8\) (and 48 can be written as 16*3 )
=> \(5^{42}*(16*3)^8\) (16 can be written as \(2^4\))
=> \(5^{42}*(2^4*3)^8\)
=> \(5^{42}*2^{4*8}*3^8\)
=> \(5^{42}*2^{32}*3^8\)
=> \(5^{10}*5^{32}*2^{32}*3^8\)
=> \(5^{10}*10^{32}*3^8\)

So, we can have 32 consecutive 0's in the end as we have \(10^{32}\) as the maximum power of 10 in the number.

So, Answer will be C
Hope it helps!

Watch the following video to MASTER Exponents

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If (125^14)(48^8) is written out as an integer, how many consecutive 10 Nov 2025, 01:26
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