Exponents Of Real Numbers — Maths STD 9 — Question
Maharashtra BoardEnglish MediumSTD 9MathsExponents Of Real Numbers1 Mark
MCQ
If $\frac{\text{x}}{\text{x}^{1.5}}=8\text{x}^{-1}$ then $x =$
A
$\frac{\sqrt{2}}{4}$
B
$\sqrt[2]{2}$
C
$4$
✓
$64$
✓
Answer
Correct option: D.
$64$
For $\frac{\text{x}}{\text{x}^{1.5}}=8\text{x}^{-1}$ we have to find the value of $x$.
So $, \frac{\text{x}^1}{\text{x}^{1.5}}=8\text{x}^{-1}$
$\text{x}^{1-1.5}8\text{x}^{-1}$
$\text{x}^{-0.5}=2^3\text{x}^{-1}$
$\frac{\text{x}^{0.5}}{\text{x}^{-1}}=2^3$
$\frac{\text{x}^{-\frac{5}{10}}}{\text{x}^{-1}}=2^3$
$\text{x}^{-\frac{1}{2}+1}=2^3$
$\text{x}^{\frac{1}{2}+\frac{2}{2}}=2^3$
$\text{x}^{\frac{-1+2}{2}}=2^3$
$\text{x}^{\frac{1}{2}}=2^3$
By raising both sides to the power $2$ we get
$\text{x}^{\frac{1}{2}\times2}=2^{3\times2}$
$\text{x}^{\frac{1}{2}\times2}=2^6$
$\text{x}^1=64$
The value of $x$ is $64$
Hence the correct alternative is $d$.
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