Question

Define the no of consecutive zeros in 2^3×3^4×5^4×7

Answer 1

we can make zero only by multiplying 2 and 5, like
2*5=10
2*2*5=20
so we can conclude here multiplication of 2 and 5 always brings 0, however no of zeros always equal to the no of 2 and 5 in the expression, whichever is minimum.
so here comes at the question, we have to find consecutive no. of zeros, for this we have to find the find the no. of 2 and 5 in the expression and answer will be minimum one.
so in the given expression,
no. of 2=3 and no. of 5 = 4
hence your answer is 3, we can make 3 consecutive zeros by solving this expression.

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Answer 2

Answer:

$2^3\times3^4\times5^4\times7\\\\= 8 \times 81 \times 625 \times 7\\\\=(81\times7)\times(625 \times 8)\\\\ =567 \times 5000\\\\=2835000$

Keep in mind , Real numbers follows Commutativity as well as Associativity with respect to Multiplication.

As, there are three consecutive Zeroes at the end of the product.

So, number of consecutive Zeroes at the end of $2^3\times3^4\times5^4\times7$ is 3.