exponential expressions

[Jand]

I'm finding exponential expressions problems really hard. I've done 100s and I still fail to get the right answer about half the time.

I just got:

"Rewrite the expression [FONT=KaTeX_Main]14⋅2​3^[FONT=KaTeX_Math]t+2​​⋅4​2^[FONT=KaTeX_Math]t−2​​[/FONT][/FONT][/FONT] in the form [FONT=KaTeX_Main][FONT=KaTeX_Math]A⋅[FONT=KaTeX_Math]B​^[FONT=KaTeX_Math]t​​[/FONT][/FONT][/FONT][/FONT]." ........................................................wrong!

I'm OK with operating on the bases, and OK operating on exponents, but I find that translating bases to exponents and vice-versa really trips me up (creating exponents to change/reduce/eliminate/create bases or creating bases to change/reduce/eliminate/create exponents) - that is.

I'm fed up of failing - has anybody got any simple rules I can employ to help me with exponential expressions at about Algebra 1 / 2 level please?
exponential expressions

exponential expressions

 

[Steven G]

I'm finding exponential expressions problems really hard. I've done 100s and I still fail to get the right answer about half the time.

I just got:

"Rewrite the expression [FONT=KaTeX_Main]14⋅2​3^[FONT=KaTeX_Math]t+2​​⋅4​2^[FONT=KaTeX_Math]t−2​​[/FONT][/FONT][/FONT] in the form [FONT=KaTeX_Main][FONT=KaTeX_Math]A⋅[FONT=KaTeX_Math]B​^[FONT=KaTeX_Math]t​​[/FONT][/FONT][/FONT][/FONT]." ........................................................wrong!

I'm OK with operating on the bases, and OK operating on exponents, but I find that translating bases to exponents and vice-versa really trips me up (creating exponents to change/reduce/eliminate/create bases or creating bases to change/reduce/eliminate/create exponents) - that is.

I'm fed up of failing - has anybody got any simple rules I can employ to help me with exponential expressions at about Algebra 1 / 2 level please?
exponential expressions

exponential expressions

Might you mean that you want to write in the form A*B^t + C*D^t??
So the term 14*23^t is ok with A=14 and B=23. So we need to do the same with 2*42^(t-2). The problem here is the power of 42 is t-2 and not t. So what does 42^(t-2) mean? It mean 42*42*42....*42, t-2 times.
If we had 2 more factors of 42, like (42*42*42....*42)*42*42, then we would be multiplying 42 by itself (t-2)+2=t times and then we can write 42^t.
But we can't just multiply 42*42 (which is 42^2), we would have to divide by 42^2 as well. This is because 42^2/42^2 =1 and we can ALWAYS multiply by one without changing the value.
In fact, I have this saying--If you want to change the way something looks like (and YOU do since you want 42^(t-2) to become 42^t) then you multiply by one.
So 2*42^(t-2)=2(1/42^2)(42^2)(42^(t-2))=(2/42^2)(42^2) [what is in red equals 1]-->so C=2/42^2 (simplify if you like) and D=42. We now have 14*23^t + (2/42^2)(42*t).

Good luck,
Jomo

 

[stapel]

I'm finding exponential expressions problems really hard. I've done 100s and I still fail to get the right answer about half the time. I just got:

"Rewrite the expression [FONT=KaTeX_Main]14⋅2​3^[FONT=KaTeX_Math]t+2​​⋅4​2^[FONT=KaTeX_Math]t−2​​[/FONT][/FONT][/FONT] in the form [FONT=KaTeX_Main][FONT=KaTeX_Math]A⋅[FONT=KaTeX_Math]B​^[FONT=KaTeX_Math]t​​[/FONT][/FONT][/FONT][/FONT]." ........................................................wrong!

Well, then doing one more exercise for you probably isn't going to make any difference. Instead, we need to see what you're doing, so we can try to help you find where things are going sideways.

So please reply with a clear statement of what you have tried, showing all of your steps, so we can begin to provide useful assistance. Please be complete. Thank you!