Question

How does 3^x + 3^x + 3^x = 3^x+1 ?

Answer 1

it is making use of the rule:\[a\times a^n=a^{n+1}\]

Answer 2

can you see how?

Answer 3

Not really. Could you put the equation into that rule? I think I'l be able to understand, then.

Answer 4

ok, first of all how can you simplify the left hand side of your expression?

Answer 5

e.g. a + a + a = ?

Answer 6

3(3^x), right?

Answer 7

correct

Answer 8

now apply the rule

Answer 9

Lets see this question like this.... :)
let 3^x=y..... the above equation is.......
3^x + 3^x + 3^x = 3^x *3
y+y+y=y(3)
3y=3y...... It is an identity...... :DA

Answer 10

a(a^n) = a^n+1
3(3^x) = 3^x+1
Aa.
If I may ask, how does the rule work/make sense?

Answer 11

e.g.:\[a\times a^3=a\times(a\times a\times a)=a\times a\times a\times a=a^4\]

Answer 12

and 4 = 3 + 1

Answer 13

the general rule here is:\[a^m\times a^n=a^{m+n}\]

Answer 14

Ohhhh.
That makes complete sense when worked out.
Thank you so much for helping me with this concept, asnaseer!

Answer 15

yw :)