Simply multiply.

Algebra Level 2

What is the sum of the digits of the product of $3^6 \times 2^4 \times 5^7$ ?

21 18 20 19

2 solutions

Niranjan Khanderia
Aug 13, 2014

$3^6*2^4*5^7=(3^2)^3*10^4*5^3=9^3*10^4*5^3=9^3*10^4*5^3\\ =45^3*10^4=911250000,~~~~\sum =18\\ \boxed{18}$

Because of the test choices given, it is enough to observe that the number is divisible by $9$ , hence the sum of the digits is also divisible by $9$ , and $\boxed{18}$ was the only choice divisible by $9$ .

mathh mathh - 6 years, 10 months ago

Wow!Didn't notice that!!:D

Anik Mandal - 6 years, 10 months ago

What does (sum symbol) mean? How its work?

rati cristy - 6 years, 7 months ago

$\sum_{n=1}^{4} (n+1)$ it means that first, we will start with replacing n. n= 1. start with 1, 1+1=2, 2+1=3,3+1=4,4+1=5. end in 4.now add these values, 2+3+4+5 = 14 $\sum_{n=1}^{4} (n+1)=14$ it is used to add numbers in sequence

Aareyan Manzoor - 6 years, 7 months ago

Rakshit Pandey
Aug 15, 2014

On rearranging,
$3^6 \times 2^4 \times 5^7 = (2 \times 3 \times 5)^4 \times (3 \times 5)^2 \times 5$
Solving,
$\Rightarrow 3^6 \times 2^4 \times 5^7 = (30)^4 \times (15)^2 \times 5$
$\Rightarrow 3^6 \times 2^4 \times 5^7 = (810000) \times (225) \times 5$
$\Rightarrow 3^6 \times 2^4 \times 5^7 = (4050000) \times (225)$
$\Rightarrow 3^6 \times 2^4 \times 5^7 = 911250000$

Simply multiply.

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