Having unlocked the door, Tom proceeded to battle with his combatant. Tom realized that he would need some ammunition [bullets] to counter his opponent. He found a chest full of ammunition which had a display on it. It had four buttons on it, A, B, C and D and on each button, there were some laws [equations which are always true]. The chest would open only if Tom pressed ALL the buttons with a correct law on it.

The laws on each button are given in the options – choose all the correct ones to help Tom open the chest.

$a^m \times a^n = a^{mn}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{a^m}{a^n} = a^{\frac{m}{n}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$a^m \times a^n = a^{(m+n)}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\frac{a^m}{a^n} = a^{(m-n)}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
C
$a^m \times a^n = a^{(m+n)}$

D
$\frac{a^m}{a^n} = a^{(m-n)}$

$a^{m} \times a^{n} = a^{m n}$ is false as we know that $a^{m} \times a^{n} = a^{(m + n)}$

$\frac{a^{m}}{a^{n}} = a^{\frac{m}{n}}$ is false as we know that $\frac{a^{m}}{a^{n}} = a^{(m - n)}$

$a^{m} \times a^{n} = a^{(m + n)}$ is ture

$\frac{a^{m}}{a^{n}} = a^{(m - n)}$ is true.

Hence he must press the buttons C and D.

Suggest Corrections

Similar questions

After completely filling the jet pack, Tom flew to the apex of the structure and retrieved the chip. He left the structure and now he had to demolish the entire building. To do this, he had a remote – on which, he had to touch all the equal valued buttons, as given in the given options. The game would be over once the building is demolished and Tom would win.

Choose the option which Tom should touch to demolish the structure:

After getting the code, Tom got past the commando to enter the structure. This was the final level.He was supposed to find the chip which contained military grade secrets and retrieve it. After Tom retrieves the chip, he was supposed to destroy the entire structure and leave no traces of it.

He had to fix a certain amount of C4 explosives on all the 4 walls of the structure.He had to choose one pair of equal amounts of C4 on two walls.

There was C4 explosive material packed in 4 boxes and the amount of C4 inside each box was specified in the “power” notation. Select the options which have equal amounts of C4 –

Tom now had access to the ammunition [ammo]. He now had to load a correct amount of ammo to shoot the combatant. The gun calculated the amount of ammo to be loaded and displayed the following to Tom –

“There are 27 bullets that can be fired in each roundand 64 rounds are available, which means $27 \times 64 = 2^{x} \times 3^{y}$ bullets can be shot”

The gun can be activated digitally by entering another passcode, which is the numerical value of (x-y).

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

___

Since it was a Sunday, Tom and his friends had enough time to play many more games. Tom opened a game on his computer in which, to proceed further in the game, the player would have to answer some questions.

In the first level of the game, Tom has to drive a car and reach a destination.

To get the car unlocked, he has to fill the box (in green) with any of the symbols <, >, = or $\neq$ .

What should Tom enter so that the relation between $153^{0}$ [153 raised to the power 0] and $154^{0}$ [154 raised to the power 0] holds good?

What is the value of the expression $\frac{a^{m}}{a^{n}}$ ?

Join BYJU'S Learning Program

The correct options are C D am×an=amn is false as we know that am×an=a(m+n) aman=amn is false as we know that aman=a(m−n) am×an=a(m+n) is ture aman=a(m−n) is true. Hence he must press the buttons C and D.