Question

the no of consecutive zeroes in 2 to the power 3 x 3 to the power 4 x 5 to the power 4 x 7 is?

Answer 1

Hi there!
Here's the answer:

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Type of Problem:
To find No. of zeroes at End of product

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Approach to Problem:

• Resolve the given no. into their factors
• Count No. of 2's and 5's ie., (5)^x × (2)^y.
• No. of zeroes at the End of Product = No. of 2's or 5's, whichever is less
= x; if x<y
= y; if y<x

*** Here, we are considering only (5)^x × (2)^y part of factors as product of 2& 5 places a zero at the end.

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Now, Coming to this question
No. of zeroes in 2³ × 3⁴ × 5⁴ × 7
Here, consider only 2³ × 5⁴
3<4
•°• No. of consecutive zeroes in product 2³ × 3⁴ × 5⁴ × 7 = 3

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Verification:

2³ × 3⁴ × 5⁴ × 7
= 8 × 81 × 625 × 7
= 2835000

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:)
Hope it helps