1. anonymous

$(3^{-1}-2^{-1})^{-1}$

2. DecentNabeel

1/(1/3 -1/2) $\left(-2^{-1}+3^{-1}\right)^{-1}=-6$

3. anonymous

ya, i did it on my calc and its -6

4. anonymous

|dw:1437259855827:dw|

5. anonymous

is that the way to do it? I know there are other ways to do it but is this viable?

6. anonymous

$\left( 3^{-1}-2^{-1} \right)^{-1}=\left( \frac{ 1 }{ 3^1 }-\frac{ 1 }{ 2^1 } \right)^{-1}$ $=\left( \frac{ 2-3 }{ 6 } \right)^{-1}=\left( \frac{ -1 }{ 6 } \right)^{-1}=\frac{ \left( -1 \right)^{-1} }{ \left( 6 \right)^{-1} }=\frac{ 6^1 }{ \left( -1 \right) }$=-6

7. anonymous

how about the way i did it? is that okay too?

8. anonymous

????

9. anonymous

no

10. anonymous

o...

11. anonymous

$x^a=\frac{ 1 }{ x ^{-a} }~and~viceverse$

12. DecentNabeel

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}$ $=\left(-\frac{1}{2}+\frac{1}{3}\right)^{-1}$

13. DecentNabeel

$\left(-\frac{1}{2}+\frac{1}{3}\right)^{-1}=\frac{1}{-\frac{1}{2}+\frac{1}{3}}$ $\mathrm{Combine\:the\:fractions\:using\:the\:LCD}:\quad -\frac{1}{2}+\frac{1}{3}=\frac{2-3}{6}$

14. DecentNabeel

$=\frac{1}{-\frac{1}{6}}$ =-6

15. DecentNabeel

are you understand @yomamabf