brackets

**andyboy179** · October 22nd 2009, 07:30 AM

how would i work this out?

$(4^2)$

**ramiee2010** · October 22nd 2009, 07:34 AM

$(4^2)=(4\times 4)=16$

**andyboy179** · October 22nd 2009, 07:36 AM

Originally Posted by ramiee2010

$(4^2)=(4\times 4)=16$

thanks! $(4^{-2})^{-3}$ would that be 24???

**ramiee2010** · October 22nd 2009, 07:42 AM

$(4^{-2})^{-3}=(4^{(-2 )\times ( -3)})=4^6=4096$

**andyboy179** · October 22nd 2009, 07:45 AM

Originally Posted by ramiee2010

$(4^{-2})^{-3}=(4^{(-2 )\times ( -3)})=4^6=4096$

wouldn't you do 4X-2= -8 -8X-3= 24?

**ramiee2010** · October 22nd 2009, 07:55 AM

Originally Posted by andyboy179

wouldn't you do 4X-2= -8 -8X-3= 24?

do you know that $a^{-1} =\frac{1}{a} \Rightarrow a^{-2} =\left (\frac{1}{a} \right )^2=\frac{1^2}{a^2}=\frac{1}{a^2}$
$4^{-2} =\left (\frac{1}{4} \right ) ^2 =\left (\frac{1^2}{4^2} \right ) =\left (\frac{1 \times 1}{4 \times 4} \right )=\left (\frac{1}{16} \right )$
$(4^{-2})^{-3} = \left (\frac{1}{4^2} \right )^{-3} = \left ( \frac{1}{(\frac{1}{4^2})} \right )^3=(4^2)^3=4^{(2 \times 3)}=4^6$

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