Question

Explain how to find the number of zeros in the product for exercise 14

Answer 1

Answer:

Of which class and which book

Answer 2

Answer:

Zero exists as a number, and the numerical digit exists utilized to express that number in numerals. It fulfills a prominent role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 exists utilized as a placeholder in place value systems.

Step-by-step explanation:

If the end of a product or the unit digit of a number exists at zero, it indicates it exists divisible by 10, that exists it is a multiple of 10. So, the number of zeros at the end of any number exists equivalent to the number of times that number can be factored into the power of 10.

Example

Number of zeros = Number of pairs of $2 \times 5$

$&56^{99} \times 125^{89}=\left(2^{3} \times 7\right)^{99} \times\left(5^{3}\right)^{89}$

$&\Rightarrow 2^{297} \times 7^{99} \times 5^{267}$

$&\Rightarrow(2 \times 5)^{267} \times 2^{30} \times 7^{99}$

$&\Rightarrow 10^{267} \times 2^{30} \times 7^{99}$

Therefore, the number of zeros in the given product exists at 267.

In the case of only multiplication

Number of Zeros = min{a, b}

where a exists the maximum power of 2 and b exists the maximum power of 5.

Number of Zeros = min {297, 267} = 267.

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