Question

Question 14

Which of the following is not equal to ${\left(\frac{-5}{4}\right)}^4$?
(a) $\frac{(-5{)}^4}{4^4}$
(b) $\frac{5^4}{(-4{)}^4}$
(c) $-\frac{5^4}{4^4}$
(d) $(-\frac{5}{4})\times (-\frac{5}{4})\times (-\frac{5}{4})\times (-\frac{5}{4})$

Answer 1

We know that, ${\left(\frac{p}{q}\right)}^m=\frac{p^m}{q^m}So,{\left(\frac{-5}{4}\right)}^4=\frac{(-5{)}^4}{(4{)}^4}or\left(\frac{-5}{4}\right)=\frac{(5{)}^4}{(-4{)}^4}or{\left(\frac{-5}{4}\right)}^4=\left(\frac{-5}{4}\right)\times \left(\frac{-5}{4}\right)\times \left(\frac{-5}{4}\right)\times \left(\frac{-5}{4}\right)$
Hence, option (c) is not equal to ${\left(\frac{-5}{4}\right)}^4$.