Question 184376
<font face="Times New Roman" size="+2">


Missed it by <i><b>that</b></i> much.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \[\frac{(9a^3)}{(10b^4)}\]^{-2}]


You only applied the -2 exponent to the denominator, when the square brackets are around the entire fraction.  That is to say, your answer would have been (almost) correct if you had started with:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \[\frac{(9a^3)}{(10b^4)^{-2}}\]]


So, first apply the following rule:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}]


Giving you:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \frac{(9a^3)^{-2}}{(10b^4)^{-2}}]


Next apply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ (a^m)^n = a^{mn}]


(Which you did correctly where you applied it) Giving you:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \frac{9a^{-6}}{10b^{-8}}]


But you still have one more step, and this is why I added the parenthetical <i>almost</i> earlier:


Apply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ a^{-n} = \frac{1}{a^n}]


Giving you:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \frac{10b^8}{9a^6}]


John
*[tex \Large e^{i\pi} + 1 = 0]
</font>