Question

what is the highest power of 2 in the expression (1800*25*4^5*21^2*45^2)
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Answer 1

Answer:

the higest power of 2 is 10 i am aure

Answer 2

$Given \: expression\: [1800\times 25 \times 4^{5} \times (21)^{2} \times (45)^{2}]$

$= ( 2^{3} \times 3^{2} \times 5^{2} ) \times 5^{2} \times (2^{2})^{5} \times ( 3 \times 7)^{2} \times ( 3^{2} \times 5 )^{2} \\= 2^{3} \times 3^{2} \times 5^{2} \times 5^{2} \times 2^{10}\times 3^{2} \times 7^{2} \times 3^{4} \times 5^{2} \\= 2^{3+10}\times 3^{2+2+4} \times 5^{2+2+2} \times 7^{2}$

$\boxed{ \pink{ \because a^{m} \times a^{n} = a^{m+n} }}$

$= 2^{13} \times 3^{8} \times 5^{6} \times 7^{2}$

Therefore.,

$\red{ Highest \: power \: of \: 2 \:in \: the }\\\red{ expression } \green { = 13}$

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