Question

Evaluate

1.  {\((\frac{1}{3})^{−1} − (\frac{1}{4})^{−1}\)}⁻¹ 
2.  \((\frac{5}{8})^{−7}× (\frac{8}{5})^{−4}\)

Answer 1

(i) {\((\frac{1}{3})^{−1} − (\frac{1}{4})^{−1}\)}⁻¹ 

\((\frac{a}{b})^{−m} = (\frac{b}{a})^m\)

{\((\frac{1}{3})^{−1} − (\frac{1}{4})^{−1}\)}⁻¹
\(= (3^1 − 4^1)−1\)
\(= (3 − 4)^{−1}\)
\(= (−1)^{−1}\)
\(= (\frac{−1}{1})^1= −1\)

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(ii) \((\frac{5}{8})^{−7}× (\frac{8}{5})^{−4} \)

We know that, \((\frac{a}{b})^{−m} = (\frac{b}{a})^m\)

\((\frac{5}{8})^{−7}× (\frac{8}{5})^{−4} \)

\(= (\frac{8}{5})^7 × (\frac{8}{5})^{−4}\)

\(= (\frac{8}{5})^3\)      [Since, \(\frac{a^m}{a^n} = a^{m - n}\)]

\(= \frac{512}{125}\)