Jika a^(3/2) = b^(-3/2) . c^(3/4), maka c dinyatakan dalam a dan b adalah... help please? :) thanks.... Question from @gwenlauren36

October 2018 2 35 Report

Jika a^(3/2) = b^(-3/2) . c^(3/4), maka c dinyatakan dalam a dan b adalah... help please? :) thanks

izharulhaq78 $\displaystyle a^{\frac32}=b^{-\frac32}\times c^{\frac34}\\a^{\frac32}=\frac1{b^{\frac32}}\times c^{\frac34}\\a^{\frac32}\times b^{\frac32}=c^{\frac34}\\(ab)^{\frac32}=c^{\frac34}\\(ab)^{\frac32\times\frac{4}{3}}=c\\(ab)^{1\times2}=c\\(ab)^{2}=c\\\boxed{\boxed{a^{2}b^{2}=c}}$

3 votes Thanks 7

bgimma33 $$\begin{align}a^{\displaystyle\frac{3}{2}}~~&=~b^{\displaystyle-\frac{3}{2}}~\bullet~c^{\displaystyle\frac{3}{4}} \\ \\ &~~\bold{kita~tukar~posisi~agar~c~berada~sendirian} \\ \\ c^{\displaystyle\frac{3}{4}}~~&=~\frac{a^{\displaystyle\frac{3}{2}}}{b^{\displaystyle-\frac{3}{2}}} \\ \\ c^{\displaystyle\frac{3}{4}}&=~\bold{(ab)^{\displaystyle\frac{3}{2}}}\end{align}$

$\bold{c^{\displaystyle\frac{\not3^1}{\not4^1}~\times~\frac{\not4^1}{\not3^1}}~~=~~(ab)^{\displaystyle\frac{\not3^1}{\not2^1}~\times~\frac{\not4^2}{\not3^1}}} \\ \\ \bold{c~~=~~(ab)^2~~=~~a^2~b^2}$

2 votes Thanks 4

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