How to solve indices with fractions in maths.

Welcome to my channel. Good day, everyone. We are asked to find the value of t for which 64 over 27 Is equal to 3 over 4 raised to the power of t minus 1. Okay, let's go ahead and get the solution. Okay, now looking at this question, it seems somewhat Tactical, but it's very easy. Let's do that. solution Okay, let me do this side We have 64 over 27 equal to what 3 over 4 raised to the power of t Minus 1 now, first of all, I want to do something so that this side looks like this. Then an idea came to my mind What is it that we can do? What number raised to the power of 4 gives 64, or raised to the power of 3 gives 64? You can say that 4 raised to the power of 3 is 64. Let's check 4 times 4 is 16, 16 times 4. Let's see, 4 times 6 is 24, right? 4 times 1 is 4, plus 2 is 6, so you see that 4 raised to the power of 3 will give us what? 64, so we set this one aside; 4 raised to the power of 3, then for 27 3 raised to the power of 3 is 27, right? 3 times 3 is 9, 9 times 3 is what, 27? So 27 is 17 as 3 raised to the power of 3 So I'm going to replace this 64 now with 4 raised to the power of 3. So I'm going to write 4 raised to the power of 3 all over 27 is what 3 raised to the power of 3 equals, in parentheses, 3 raised to the power of 4 3 over 4 raised to the power of t Minus 1 now, let's go ahead and solve this. Okay, but when I look at this, we can't write that. 4 over 3 raised to the power of 3 because this is 3 and this is 3, right, is equal to 3 over 4. raised to the power of 3 -1 Looking at this, I want them to look alike. How do we do that? 4 over 3 raised to the power of 3 can be written as if I should invert it That is, if I should write 3 over 4 It will now become raised to the power of minus 3, which is equal to 3 over 4. Raised to the power of t minus 1 All right You can see that I actually am able to establish the same thing here and here. So we can say that if this is equal to this, then their powers are also equal. Okay, let's go ahead and Get the solution Now, looking at this, if this and this are equal, that means minus 3 is equal to t minus 1. Okay, so we can write that minus 3 is equal to t minus 1 now We can write that how do we get our t for t to be alone? This minus 1 is going to stay here and cross the equation sign. Come and meet what minus 3, and if it does that, this minus sign we change to positive. So I'm going to have that minus 3 plus 1 is equal to t now minus 3 plus 1 is sentinels 1 minus 2 We should give you what's minus 2, so I have that minus 2 is equal to what see That is your final. You do have a lovely day and Bye