Question

Simplify:${\left(0.0001\right)}^{\frac{-3}{4}}$

• A. $20$
• B. ${10}^{-3}$
• C. $1000$
• D. $100$

Answer 1

The correct option is C

$1000$

Simplification:

$$\begin{gathered} {\left(0.0001\right)}^{\frac{-3}{4}}={\left(\frac{1}{10000}\right)}^{\frac{-3}{4}} \\ \Rightarrow {\left(0.0001\right)}^{\frac{-3}{4}}={\left(\frac{1}{{10}^4}\right)}^{\frac{-3}{4}} \\ \Rightarrow {\left(0.0001\right)}^{\frac{-3}{4}}={\left({10}^4\right)}^{\frac{3}{4}} \\ \Rightarrow {\left(0.0001\right)}^{\frac{-3}{4}}={10}^3=1000 \end{gathered}$$$\left[\because \frac{1}{a^m}=a^{-m}\right]$

Final answer: Hence, option C is correct.