## anonymous one year ago Evaluate. [9/4]^-1/2 I'm not sure how to solve this one because its' a fraction.

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1. UsukiDoll

$\LARGE (\frac{9}{4})^{-\frac{1}{2}}$ is this your question? can you see the latex?

2. anonymous

43. B

3. Astrophysics

$\huge \left( \frac{ a }{ b } \right)^{-m} \implies \left( \frac{ b }{ a } \right)^m$ use this

4. Astrophysics

So you should be able to evaluate, another thing $\huge \left( \frac{ b }{ a } \right)^m = \frac{ b^m }{ a^m }$

5. anonymous

4^1/2 / 9^1/2

6. UsukiDoll

I would've just use the negative exponent rule $\LARGE (\frac{9}{4})^{-\frac{1}{2}}$ $\LARGE \frac{1}{(\frac{9}{4})^{\frac{1}{2}}}$ then change the bottom to radical form

7. UsukiDoll

$\LARGE \frac{1}{\sqrt{\frac{9}{4}}}$

8. UsukiDoll

what is the square root of 9 what is the square root of 4

9. anonymous

3 and 2

10. anonymous

But what do I do with those

11. Astrophysics

Ok so you have $\left( \frac{ 3 }{ 2 } \right)^{-1} \implies \left( \frac{ 2 }{ 3 } \right)^1 = \frac{ 2 }{ 3 }$ as shown by the property above

12. Astrophysics

Or if you are doing it usuki's way $\huge \frac{ 1 }{ \frac{ a }{ b } } \implies \frac{ b }{ a }$ which is the same as above haha.

13. anonymous

Thank you both so much, can y'all medal each other? I can only medal one person but I'm grateful for both of your help.

14. UsukiDoll

thanks @Astrophysics for finishing this problem while I was away.

15. Astrophysics

Np, and don't worry about medals I always got Usuki's back on those xD