Question

Find the number of zeros in the expression 15*32*25*22*40*75*98*112*125

7
12
9
14; Find the number of zeros in the expression 15*32*25*22*40*75*98*112*125; 7; 12; 9; 14

Answer 1

I think this is 10 or 12

Answer 2

Answer:

Number of zeros = 9

C is correct.

Step-by-step explanation:

Given expression,

$15\times32\times25\times22\times40\times75\times98\times112\times125$

Number of zeros in the simplified form of expression.

As we know get zero at last with multiply 2 and 5

So, first we factor each number in expression and then see number of 2 and 5

$3\cdot5\cdot2^5\cdot5^2\cdot11\cdot2\cdot2^3\cdot5\cdot5^2\cdot3\cdot7^2\cdot2\cdot2^4\cdot7\cdot 5^3$

using exponent law to add exponent of same base

$a^m\cdot a^n=a^{m+n}$

$\Rightarrow 3^2\cdot2^{14}\cdot5^{9}\cdot7^3\cdot 11$

Now we check number of 2 and 5 because product of 2×5=10

$\Rightarrow 2^{14}\cdot5^{9}$

The number has less exponent will show number of zeros.

So, 2's exponent 14 and 5's exponent 9

So, Number of zeros = 9