Question

Express as a power of a rational number ${\left({\left(\frac{-3}{2}\right)}^{-2}\right)}^{-3}$

• A. ${\left(\frac{-3}{2}\right)}^6$
• B. ${\left(\frac{2}{3}\right)}^{-6}$
• C. ${\left(\frac{-3}{2}\right)}^{-6}$
• D. ${\left(\frac{2}{3}\right)}^6$

Answer 1

Answer: (A), (B)

The correct options are
A ${\left(\frac{-3}{2}\right)}^6$
B ${\left(\frac{2}{3}\right)}^{-6}$

Using laws of exponents,$(a^m{)}^n=(a{)}^{m\times n}and{a}^{-m}=\frac{1}{a^m}\therefore {\left({\left(\frac{-3}{2}\right)}^{-2}\right)}^{-3}={\left(\frac{-3}{2}\right)}^{-2\times (-3)}={\left(\frac{-3}{2}\right)}^6={\left(\frac{-2}{3}\right)}^{-6}$