Question

Having entered the passcode correctly, Tom got his mission. He needs to fight an enemy combatant and get information about the next clue. Tom found the room where the combatant was, but to enter the room, he needed another passcode.The passcode is the answer to the following display:

“The lock thinks that 0.36 = 3 $\times$ ${10}^a$ + 6 $\times$ ${10}^b$ and the passcode is the value (a $\times$ b)”

What is the passcode that Tom has to enter? ______ [Enter a numerical value]

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Answer 1

$0.36=3\times {10}^a+6\times {10}^b$ is what is being given.
Now, we know that $0.36=0.3+0.06$
$=\frac{3}{10}+\frac{6}{100}=\frac{3}{{10}^1}+\frac{6}{{10}^2}$
$=3\times {10}^{-}1+6\times {10}^{-}2$ (since $\frac{1}{a^m}=a^{-m}$)
Thus, since $0.36=3\times {10}^a+6\times {10}^b$, a = -1 and b = -2
$a\times b=-1\times -2=2$