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Which is the correct prime-power form of 3600?

Class 7Prime Factors in Exponent FormNumber System

A $2^{2} \times 3^{2} \times 5^{4}$
B $2^{3} \times 3^{2} \times 5^{2}$
C $2^{4} \times 3^{3} \times 5^{2}$
D $2^{4} \times 3^{2} \times 5^{2}$

Step-by-Step Solution

3600 =

36 \times 100 = (2^{2} \times 3^{2}) \times (2^{2} \times 5^{2}) = 2^{4} \times 3^{2} \times 5^{2}

. Check:

16 \times 9 \times 25 = 3600

. The second option gives 1800.

Answer: D)

2^{4} \times 3^{2} \times 5^{2}

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