Question

\[\left( \frac{2}{3} \right)^{- 5}\] is equal to

Options

• \[\left( \frac{- 2}{3} \right)^5\]

   

• \[\left( \frac{3}{2} \right)^5\]
• \[\frac{2x - 5}{3}\]
• \[\frac{2x - 5}{3}\]

Answer 1

\[\left( \frac{3}{2} \right)^5\]
Rearrange (2/3)⁻⁵ to get a positive exponent.
\[\left( \frac{2}{3} \right)^{- 5} = \frac{1}{\left( \frac{2}{3} \right)^5} \left( a^{- n} = \frac{1}{a^n} \right)\]
\[ = \frac{1}{\frac{2^5}{3^5}} \left\{ \left( \frac{a}{b} \right)^n = \frac{a^n}{b^n} \right\}\]
\[ = \frac{3^5}{2^5}\]
\[ = \left( \frac{3}{2} \right)^5\]