# Powers

Discussion in 'Mathematics' started by elizabeth1972, Jun 5, 2012.

1. ### elizabeth1972

I'm a primary teacher helping my Y10 son to revise for his modular GCSE maths exams.
Could any kind soul please explain to me in a way I can re-explain to him...

Write as a power of 4
45 x 47 (45)3

and, find the value of n
<font face="Calibri"></font>3n = 1/9 Any help would be very gratefully recevied!

2. ### elizabeth1972

I'm a primary teacher helping my Y10 son to revise for his modular GCSE maths exams.
Could any kind soul please explain to me in a way I can re-explain to him...

Write as a power of 4
45 x 47 (45)3

and, find the value of n
<font face="Calibri"></font>3n = 1/9 Any help would be very gratefully recevied!

3. ### maths126New commenter

Often the best way to understand these is to write them out in full initially, rather than rush to apply some fancy rule or short cut straight away without thinking.
4^5 = 4 x 4 x 4 x 4 x 4
4^7 = 4 x 4 x 4 x 4 x 4 x 4 x 4
Multiplying these two together:
= 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4
= 4 ^ 12
Notice that this is the same as 4^(5+7) - the 'add the powers' rule.

(4^5)^3 = (4^5) x (4^5) x (4^5)
= 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4
= 4^15
Notice that this is the same as 4^(5*3) - the 'multiply the powers' rule.

For the last one, it's a good idea to start on the right.
(1/9) = (1/3) x (1/3)
But we know that (1/3) can be written as 3^(-1)

So we have (1/9) = 3^(-1) x 3^(-1)
Applying the 'add the powers' rule, we now get:

3^( (-1) + (-1) )
= 3^(-2)

So we have found n.

I'm primary too but I think this is right!

4^5 is 4x4x4x4x4
4^7 is 4x4x4x4x4x4x4
so 4^5x4^7 is 4x4x4x4x4x4x4x4x4x4x4x4 which is 4^12
4^5 is 4x4x4x4x4
so 4^5 cubed is (4x4x4x4x4) x(4x4x4x4x4) x(4x4x4x4x4)
which is 4^15
3^2=1x3x3=9
3^1=1x3=3
3^0=0x3=0
3^-1=1/3
3^-2=1/(3x3) =1/9

5. ### Colleen_YoungOccasional commenter

45 x 47
4x4x4x4x4 x 4x4x4x4x4x4x4 = 412
if you think about it - just add the powers when multiplying (assuming base number is the same).

(45)3
= 45 x 45 x 45
= 4x4x4x4x4 x 4x4x4x4x4 x 4x4x4x4x4 = 415
power to a power - multiply the indices
for the rules of indices, have a look at David's PowerPoint on Laws of Indices here
Need to work out how to format answer to last question!

It took me ages to type that out and someone got there first

7. ### Colleen_YoungOccasional commenter

3 replies all at about the same time!

8. ### elizabeth1972

This is what I thought, but my son is convinced that he's trying to find an answer where the "power" is 4, e.g. x^4 ?????

9. ### Colleen_YoungOccasional commenter

All the above replies are correct answers to your questions. It's 4 to the power what?!
The power is not 4.
See Craig Barton's notes - scroll down to negative indices for help with your third question.

10. ### lolo7129

...and not one of them saying "Do you really not know that as the first one is a C grade GCSE question?"
Good responses by people.

11. ### elizabeth1972

I did know the answer to the first one, but my son had me convinced I was wrong.
Thanks for all the help - we were trying to make it more difficult than it was here!

12. ### Colleen_YoungOccasional commenter

abed mymaths is a paid for subscription service - there is no way you should be publishing login details here - I suggest you ask TES to remove this very fast.

13. ### elizabeth1972

Thanks, but we have a mymaths login though his school. We were just getting panicky because I thought I knew how to work it out (and it seems that I was right!) but he was trying to convince me otherwise.