Question

If $\frac{p}{q}={\left(\frac{2}{3}\right)}^3÷{\left(\frac{3}{2}\right)}^{-3}$, then the value of ${\left(\frac{p}{q}\right)}^{-10}$=________.

• A. $1$
• B. $0$
• C. Cannot be determined
• D. None of the above

Answer 1

The correct option is A $1$

$\frac{p}{q}={\left(\frac{2}{3}\right)}^3÷{\left(\frac{3}{2}\right)}^{-3}$

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

Thus, $\frac{p}{q}=1$

${\left(\frac{p}{q}\right)}^{-10}=(1{)}^{-10}=1$