Question

INDICES : Expand and Simplify: can anyone check my answer?

Answer 1

\[\left( \sqrt{x}+\frac{ 1 }{ \sqrt{x} } \right)^{2}\]

Answer 2

i reckon it is \[x+2+\frac{ 1 }{ x}\]

can i simplify further though?

Answer 3

i dont think so

Answer 4

So im right?

Answer 5

Yes you're right !

Answer 6

yay! I'm also not confident about if i've simplified this correctly ....
\[(3^{n}+5^{n})(3^{n}-5^{-n})\]
It's not difference of two squares ...so do I just expand as usual?

Answer 7

\(5^{-n} = \frac{1}{5^n}\)

Answer 8

I got \[3^{2n} -(3^{n \times}5^{n})+(3^{n \times}5^{n})+5^{0}\]

Answer 9

\[3^{2n}+1\]

Answer 10

now have a second look at the given expression
isnt it like

\((x + y)(x -\frac{1}{y})\)

Answer 11

yep

Answer 12

careful, you have -n on top,
check ur calculation again

Answer 13

\(3^{2n} -(3^{n \times}5^{\color{red}{-n}})+(3^{n \times}5^{n})+5^{0} \)

Answer 14

Oh yes, I see (Woops! - its hard to keep track when typing) Yes so that is the simplest form?

Answer 15

\(3^{2n} -(3^{n \times}5^{\color{red}{-n}})+(3^{n \times}5^{n})+5^{0} \)

\(3^{2n} -(3^{n \times}\frac{1}{5^{\color{red}{n}}})+15^{n}+ 1 \)

Answer 16

\(3^{2n} -(3^{n \times}5^{\color{red}{-n}})+(3^{n \times}5^{n})+5^{0} \)

\(3^{2n} -(3^{n \times}\frac{1}{5^{\color{red}{n}}})+15^{n}+ 1 \)

\(3^{2n} -(\frac{3}{5})^n+15^{n}+ 1 \)

Answer 17

thats the final simplified form

Answer 18

OOOoooh dang - I didn't realise I could do that ahhh

Answer 19

:)

Answer 20

Ok, thanks alot - (we had an indices test today and I new I got that wrong...) better start practicing those!

Answer 21

ohh looks you already knw all the rules and stuff... just need to practice i think

Answer 22

good luck !

Answer 23

Yup.... anyway THANKYOU!!

Answer 24

np =)

Answer 25

luv your display picture btw

Answer 26

aww ty :3