Question

Which of the following is not a reciprocal of ${\left(\frac{2}{3}\right)}^4$?

• A. ${\left(\frac{3}{2}\right)}^4$
• B. ${\left(\frac{2}{3}\right)}^{-4}$
• C. ${\left(\frac{3}{2}\right)}^{-4}$
• D. $\frac{3^4}{2^4}$

Answer 1

The correct option is C

${\left(\frac{3}{2}\right)}^{-4}$

Reciprocal of a value $x$ = $\frac{1}{x}$

Here, given value is ${\left(\frac{2}{3}\right)}^4$.

So, its reciprocal = $\frac{1}{{\left(\frac{2}{3}\right)}^4}$

= $(\frac{2}{3}{)}^{-4}$ ($\because \frac{1}{a^n}=(a{)}^{-n}$)

(or)

$\frac{1}{{\left(\frac{2}{3}\right)}^4}$ = $(\frac{3}{2}{)}^4$

= $\frac{\left(3^4\right)}{\left(2^4\right)}$ $(\because (\frac{a}{b}{)}^n=\frac{a^n}{b^n})$