Question

How do I simplify ((x^(a+b))^(a-b))/((x^(a-2b))^(a+2b))

Answer 1

congrats on you first question @OdinMW

Answer 2

Thanks, Its a fraction. Im this is the only way I could write it out. Sorry for all the brakets.

Answer 3

ikr looks hard @ 1st glance

Answer 4

well you need to use the power of a power for the numerator and denominator

\[(x^a)^b = x^{a \times b}\]

once you have used the rule.. look for common factors... to cancel

Answer 5

Would the first part be x^(a^2-b^2)?

Answer 6

thats correct, well done

Answer 7

If i took (x^(a+b))^(a-b)

Answer 8

yep the index law for power of a power says multiply the powers.

Answer 9

Is the correct answer 4?

Answer 10

i think that's what i got....it took me a really long time tho -_- want me to explain...nvm cuz i saw campbell has already done so :)

Answer 11

I hope its right :) thanks for confirming!

Answer 12

thats impossible... this is what you have so far

\[\frac{x^{(a^2 - b^2)}}{(x^{(a - 2b})^{(a + 2b)}}\]

you need to use the power of a power on the numerator...

Answer 13

So on the bottom I have \[x ^{a ^{2}-4b ^{2}}\]

Answer 14

Which makes it \[\frac{ x ^{a ^{2}-b ^{2}} }{ x ^{a ^{2}-4b ^{2}} }\]

Answer 15

thats correct

Answer 16

so now you have your simplified fraction...

Answer 17

.... wait

Answer 18

now you need to use the power rule for dividing

\[\frac{x^a}{x^b} = x^{a - b}\]

Answer 19

I have to go... but you need to simplify

\[x^{(a^2 - b^2)-(a^2 - 4b^2)}\]

take care with the subtraction...

Answer 20

Would it than be

\[x ^{a ^{2}-b ^{2}-a ^{2}-({4b) ^{2}}}\]
So \[x ^{-b ^{2}+4b ^{2}}\]
So
\[x ^{3b ^{2}}\]
?

Answer 21

thats correct... well done

Answer 22

Thanks!!!!!!

Answer 23

glad to help