Gujarat BoardEnglish MediumSTD 8MATHSExponents and Powers3 Marks
Question
Find the value of $x$, so that:
$(-2)^3 \times(-2)^{-6}=(-2)^{2 x-1} $
✓
Answer
We have, $(-2)^3 \times(-2)^{-6}=(-2)^{2 x-1} $ Using law of exponents, $a^m× a^n= (a)^{m+n}$ [$\because$ a is non-zero integer]
Then, $(-2)^3 \times(-2)^{-6}=(-2)^{2 x-1} $
$ \Rightarrow(-2)^{3-6}=(-2)^{2 x-1} $
$ \Rightarrow(-2)^{-3}=(-2)^{2 x-1} $
On camparing both side,we get
$-3 = 2x - 1$
$\Rightarrow 2x = -2$
$\Rightarrow x = -1$
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