Question

(x^2/3 - x^-1/3) (x^-2/3 - x^1/3)
pls simplify. thanks! :)

Answer 1

expand the binomials

\[x^{\frac{2}{3}} \times x^{-\frac{2}{3}} - x^{\frac{2}{3}} \times x^{\frac{1}{3}} - x^{-\frac{1}{3}}\times x^{-\frac{2}{3}} + x^{-\frac{1}{3}}\times x^{\frac{1}{3}}\]

add the powers

\[x^0 - x^1 - x^{-1} + x^0 = 2 -x - x^{-1}\]

Answer 2

that was my answer too! but then my friend said it's 2-x-1/x
she's offline now so she couldn't explain it to me

Answer 3

Then what is the difference in it..
\[x^{-1} = 1/x\]...

Answer 4

\[2 - x - x^{-1} = 2 - x - 1/x\]

Answer 5

wait i'm sorry... how did it become\[x^0−x^1−x^−1+x^0\] ? :D

Answer 6

ohh you took out the denominator! i see!

Answer 7

It is because, In Multiplication, if bases are same, their powers add up..
\[x^a \times x^b = x ^{a+b}\]