indices-sequences and series (1 Viewer)

[kr73114]

I know how to do basic indices but I don't understand simplifying when the base numbers are the same, evaluating, etc.
Can someone explain as much as you can about indices or tell me a useful website?

 

[Tofuu]

as in a^2 x a^3 = a^5 kind of stuff?

 

[kr73114]

stuff like:
64^x=4 ...and
(16/49)^-3/2

 

[cutemouse]

64^x=4

Method 1:
64^x=4
64^x=64^(1/3)
x=1/3

Method 2:
64^x=4
x log64=log4
x= log4/log64
x=1/3

 

[kr73114]

is this right...?
when 4^x=8

step 1: (2*2^2)^x=2^3
step 2: i'm not sure

 

[cutemouse]

4^x=8

Method 1:
4^x=8
4^x=4^(3/2)
x=3/2

Method 2:
4^x=8
x log4 = log8
x=log8/log4
x=3/2

 

[tommykins]

is this right...?
when 4^x=8

step 1: (2*2^2)^x=2^3
step 2: i'm not sure

try to do 8 = 2^3
so 4^x = (2^2)^x = 2^2x = 2^3

2x=3
x=3/2

 

[kr73114]

does anyone know what this means...?
Expand and simplify, answering without using negative indices:
(x+5x^-1)^2

 

[Drongoski]

free of negative indices.

 

[kr73114]

i'm sorry if i'm asking too many questions but,
how would you take appropriate powers of both sides?
eg. b^1/3=1/7
or
n^-2=121

 

[addikaye03]

i'm sorry if i'm asking too many questions but,
how would you take appropriate powers of both sides?
eg. b^1/3=1/7
or
n^-2=121

Ok well:

b^1/3=1/7

(b^1/3)^3=(1/7)^3 [cubing both sides]

b=1/7^3=1/343

Similarly n^-2=121

(1/n^2)=121 therefore by rearranging

n^2=1/121 (n^2-1/121=0, so it's a difference of squares)

n= +1/11 or -1/11

Alternatively: If you're looking for quick indice ways

n^-2=1/121

raise each side to the power of -1/2

(n^-2)^-1/2=(1/121)^-1/2 (on the lhs the indices resolve to 1)

n=1/sqrt(11)= +-(1/11)

 

[kr73114]

I was wondering how to simplify stuff like:
100^2n-1*25^-1*8^-1
I know how to simplify the base numbers but I don't know the next step.

 

[Drongoski]

If I read yr question right:

 

[kr73114]

how do you factorise indices things? for example, just out of the top of my head
7^n+7^n+7^2
or
2^n+2^n+2^2-2^n+2^n+2^-1

 

[kr73114]

By the way all my doubts are from Cambridge Mathematics 3 unit year 11. So for further ease of understanding in the future refer to that text book.