A trending math Olympiad question.

My lovely viewers, welcome back to my channel. Today, we are going to solve a math olympiad. Question: We are asked to simplify this without a calculator. Okay, let's get to it. Solution: solution we are told to simplify 2 raised to the power of 22 times 2 raised to the power Of 33, we are going to make use of this actually under indices, that is exponential questions, yeah so we are going to make use of a large number of indices to derive the solution; so first of all we are I'm going to split this power; the power 22 can also be split, and we can write it as 2 times 11. Okay, so this sentence has 2 raised to the power of 2 times 11 times 3 raised to the power of 3 times 11, okay, so what are we going to do next? Remember this law of indices that states that a raised to the power of m raised to the power of n is equal to a raised to the power of m times n Okay, now looking at this particular law, you notice that our question or our expression here is already in this form, okay, so let's put it in this form, let's put it in this form now to put in this form we are going to have we are going to have 2 to the power of 2 raised to the 11 to the power of 11 times 3 to the power of 3 to the power of 11, okay, it's becoming more Interesting at this point, what do we do? We notice that we have 2 to the power of 2; we get what? so this sentence has 4 to the power of 11, right, times 3 to the power of 3 is 27, this 27 to the Power of 11—that's what we have now. What do we have here? Remember another law of what I am, another. the law of indices that states that a to the power of x times b to the power of x is the same thing as (a × b) to the power of x a times b to the power of x, so we are going to have that, which means that we can rewrite this as 4 times 27 to the power of what? 11. Now, what is 4 times 27? 4 times 7 will give us 28, so we write It and carry 2: 4 times 2 gives us 8, plus 2 is 10. So that means 4 times 27 is 108. raised to the power of 11, and this is this particular question In short, thank you so much for watching, and have a great day! Bye!