1. ## inidices

I'm having diffulculty solving this indices question.. Can anyone show me how its done.

3 (
2^n+1) + 5 (2^n)
---------------------------

7 (2^n) - 3 (2^n-1)

2. Originally Posted by tim_mannire
I'm having diffulculty solving this indices question.. Can anyone show me how its done.

3 (2^n+1) + 5 (2^n)
---------------------------

7 (2^n) - 3 (2^n-1)
the 3( should be level with the rest of the question..

3. Originally Posted by tim_mannire
I'm having diffulculty solving this indices question.. Can anyone show me how its done.

3 (
2^n+1) + 5 (2^n)
---------------------------

7 (2^n) - 3 (2^n-1)
Try factorising both the numerator and denominator by 2^n

4. Originally Posted by tim_mannire
the 3( should be level with the rest of the question..
Dear tim_mannire,

Do you mean $\displaystyle \frac{3(2^{n+1})+5(2^n)}{7(2^n)-3(2^{n-1})}$ ?? If it is so first you could divide both the numerator and the denominator by $\displaystyle 2^{n-1}$. Hope you could continue from here!

5. i've tried both strategies, but I really don't understand . A worked example to simplify would be good so I can work through it and understand it. thanks

6. Originally Posted by tim_mannire
i've tried both strategies, but I really don't understand . A worked example to simplify would be good so I can work through it and understand it. thanks
Dear tim_mannire,

Can you tell me what do you get when you divide the numerator by $\displaystyle 2^{n-1}$ ?

7. Originally Posted by Sudharaka
Dear tim_mannire,

Can you tell me what do you get when you divide the numerator by $\displaystyle 2^{n-1}$ ?

3 + 5 (2^n)

8. Originally Posted by tim_mannire
3 + 5 (2^n)
Dear tim_mannire,

Incorrect. Now, $\displaystyle \frac{2^{n+1}}{2^{n-1}}=\frac{2^{2}\times2^{n-1}}{2^{n-1}}=4$ and $\displaystyle \frac{2^n}{2^{n-1}}=\frac{2\times2^{n-1}}{2^{n-1}}=2$ Did you understand? Now can you tell me the answer?

9. Originally Posted by Sudharaka
Dear tim_mannire,

Incorrect. Now, $\displaystyle \frac{2^{n+1}}{2^{n-1}}=\frac{2^{2}\times2^{n-1}}{2^{n-1}}=4$ and $\displaystyle \frac{2^n}{2^{n-1}}=\frac{2\times2^{n-1}}{2^{n-1}}=2$ Did you understand? Now can you tell me the answer?

I understand it but am struggling to apply it to the question

10. Originally Posted by tim_mannire
I understand it but am struggling to apply it to the question
Dear tim_mannire,

$\displaystyle \frac{3(2^{n+1})+5(2^n)}{7(2^n)-3(2^{n-1})}=\frac{3\left(\frac{2^{n+1}}{2^{n-1}}\right)+5\left(\frac{2^n}{2^{n-1}}\right)}{7\left(\frac{2^n}{2^{n-1}}\right)-3\left(\frac{2^{n-1}}{2^{n-1}}\right)}$ Do you understand upto this? If you understand the way of dividing which I showed in the previous thread you should be able to simplify this.

11. Originally Posted by Sudharaka
Dear tim_mannire,

$\displaystyle \frac{3(2^{n+1})+5(2^n)}{7(2^n)-3(2^{n-1})}=\frac{3\left(\frac{2^{n+1}}{2^{n-1}}\right)+5\left(\frac{2^n}{2^{n-1}}\right)}{7\left(\frac{2^n}{2^{n-1}}\right)-3\left(\frac{2^{n-1}}{2^{n-1}}\right)}$ Do you understand upto this? If you understand the way of dividing which I showed in the previous thread you should be able to simplify this.

I tried what you said and i came up with 53/23.. but i also got 22/17 with a different way.. do any of them figures sound correct.. if not what is the correct final answer so i can understand how to get it. thanks

12. Originally Posted by tim_mannire
I tried what you said and i came up with 53/23.. but i also got 22/17 with a different way.. do any of them figures sound correct.. if not what is the correct final answer so i can understand how to get it. thanks
Dear tim_mannire,

The correct answer is, $\displaystyle \frac{22}{11}=2$. I think you ought to revise laws of indices.

$\displaystyle \frac{3(2^{n+1})+5(2^n)}{7(2^n)-3(2^{n-1})}=\frac{3\left(\frac{2^{n+1}}{2^{n-1}}\right)+5\left(\frac{2^n}{2^{n-1}}\right)}{7\left(\frac{2^n}{2^{n-1}}\right)-3\left(\frac{2^{n-1}}{2^{n-1}}\right)} =\frac{3\left(\frac{2^2\times2^{n-1}}{2^{n-1}}\right)+5\left(\frac{2\times2^{n-1}}{2^{n-1}}\right)}{7\left(\frac{2\times2^{n-1}}{2^{n-1}}\right)-3\left(\frac{2^{n-1}}{2^{n-1}}\right)}$

$\displaystyle =\frac{(3\times2^2)+(5\times2)}{(7\times2)-(3\times1)}=\frac{22}{11}=2$