Question

With C4 explosives set, Tom proceeded into the structure. After he retrieves the chip, he needs to activate the C4 and bring the building down.Tom needs to reach the apex [top] of the structure, where the chip was hidden. He had a jetpack which can propel him to reach the height. However, there wasn’t enough fuel in it. Tom needs ${12}^m$ amount of fuel for the jetpack – he had only $3^m$ amount of fuel left.

What is the amount of fuel he needs to multiply to the existing fuel to reach the apex?

• A. 4^m
• B. 2^2m
• C. 6^m
• D. None of the above

Answer 1

Answer: (A), (B)

The correct options are
A

4^m

B

2^2m

He needs $(12{)}^m$ amount of fuel to reach the apex of the structure
But he has $3^m$ amount of fuel left in his pack.

Now, he needs to multiply the fuel with a certain amount, say x, to obtain ${12}^m$ amount of fuel

Thus $3^m\times x={12}^m$

Now we know that when the powers are equal, bases get multiplied in the product ($a^m\times b^m={(a\times b)}^m$)

Thus, let us define x as $x=y^m$

Now, $3^m\times y^m={12}^m$

${\left(3y\right)}^m={12}^m$

Since powers are equal, we can compare the bases.

$3y=4,hence,y=\frac{12}{3}=4$

$x=y^m=4^m$