How many digits are there in the integer 8^7 × 25^12?

Question

A. 27
B. 24 
C. 21 
D. 19 
E. 15

ronny123 · Accepted Answer

8^7 × 25^12

This can be simplified to 
2^21 × 5^24 (since 2^3 = 8 and 5^2 = 25)

Now 2 x 5 =10

So, simplifying further
(2^21 × 5^21) x 5^3
= 10^21 x 5^3
= 125 x 10^21

10^21 has 1 one and 21 zeros which when multiplied with 125 gives 125 followed by 21 zeros
So, in total, 24 digits

Correct Option: B

OptimusPrepJanielle · Answer

We can easily calculate the number of digits in teh end, if we know the number of 0's at the end.

8^7 × 25^12 = (2^3)^7*(5^2)^12 = 2^21*5^24 = 5^3*(10)^21 (Converting into the powers of 10)
= 125*10^21

Total digits = 21 0's + 3 digits = 24

Correct Option: B

gmathopeful19 · Answer

What I did was break it down to the prime numbers - 5^24 and 2^21 and took 24 as my answer bc it was the largest exponent.

I used 5^2 * 2^1 = 20 to verify my approach, but idk if it just works in this case. Is this a valid method?

Posted from my mobile device

Sirakri · Answer

8^7*25^{12}

(2^3)^7*(5^2)^{12}

2^{21}*5^{24}

(2*5)^{21}*5*5*5

125*10^{21}

That's 3+21=24 digits.

B.

JeffTargetTestPrep · Answer

Let’s prime factorize the given terms:
 
8^7 × 25^12 = (2^3)^7 x (5^2)^12 = 2^21 x 5^24
 
We see that we have 21 five-by-two pairs, which create 21 trailing zeros. 
 
We are left with 5^3 = 125, which is 3 digits.
 
Thus, 8^7 × 25^12 has a total of 21 + 3 = 24 digits.
 
Answer: B

ramblers · Answer

This is how I did it as well. I can't tell if I got lucky or if I'm a low key genius.

niks18 · Answer

Hi  jsheppa  &  gmathopeful19 ,

This is not a valid approach. as per this logic if I have  2^3*3^2 , then I should have  3  digits but  2^3*3^2=72 , i.e. two digits only.

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How many digits are there in the integer 8^7 × 25^12?

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How many digits are there in the integer 8^7 × 25^12?

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