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# Evaluating exponent expressions with variables

## Video transcript

we are asked to evaluate the expression 5 to the X power minus 3 to the X power 4x equals 2 so pause this video and see if you can figure out what happened what is this expression equal when x equals 2 all right now let's work through this together so what we want to do is everywhere we see an X we want to replace it with a 2 so this expression for x equals 2 would be 5 to the 2nd power minus 3 to the 2nd power well what's that going to be equal to well 5 to the 2nd power that's the same thing as 5 times 5 and then from that we are going to subtract 3 times 3 3 times 3 and now order of operations would tell us to do the multiplication or do the exponents first which is this multiplication but just to make it clear I'll put some parentheses here and this is going to be equal to 5 times 5 is 25 minus 9 which is equal to plus 25 minus 9 it is equal to 16 so that's what that expression equals 4x equals 2 let's do another example so now we are asked what is the value of Y squared minus X to the fourth when Y is equal to 9 and x equals 2 so once again pause this video and see if you can evaluate that alright so here we are we have variables as the bases as opposed to being the exponents and we have two different variables but all we have to do is wherever we see a y we substitute it with a 9 and wherever we see an X we substitute it with a 2 so Y squared is going to be the same thing as 9 squared minus minus X which is 2 that - looks a little bit funny let me see so there's gonna be 9 squared minus X which is 2 2 to the fourth power now what is this going to be equal to well 9 squared is 9 times 9 so this whole thing is going to be equal to 81 this whole thing right over here is 9 times 9 9 times 9 is that right over there and then from that we're going to subtract 2 to the 4th power well what's 2 to the 4th power that is 2 times 2 times 2 times 2 so this is going to be 2 times 2 is 4 4 times 2 is 8 8 times 2 is 16 so it's 81 minus 16 now what is that going to be equal to let's see 81 minus 6 is 75 and then minus another 10 is going to be 65 so there you have it Y squared minus X to the fourth when Y is equal to 9 and x equals 2 is equal to 65 and we're done