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Exponents Of Real Numbers — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSExponents Of Real Numbers1 Mark
Question
When simplified $\Big(-\frac{1}{27}\Big)^{-\frac{2}{3}}$ is:
  1. $9$
  2. $-9$
  3. $\frac{1}{9}$
  4.  $\frac{1}{9}$
✓

Answer

  1. $9$
Solution:
We have to find the value of $\Big(-\frac{1}{27}\Big)^{\frac{-2}{3}}$
So,
$\Big(-\frac{1}{27}\Big)^{\frac{-2}{3}}=\Big(-\frac{1}{27}\Big)^{\frac{-2}{3}}$
$=\Big(-\frac{1}{3^3}\Big)^{\frac{-2}{3}}$
$=-\frac{1}{3^{3\times\frac{-2}{3}}}$
$\Big(-\frac{1}{27}\Big)^{\frac{-2}{3}}=-\frac{1}{3^{-2}}$
$=-\frac{1}{\frac{1}{3^2}}$
$=\frac{1}{\frac{1}{9}}$
$=9$
Hence the correct choice is a.

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