Question

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

• A. $1$
• B. $0$
• C. $-1$
• D. Cannot be determined

Answer 1

Answer: (A)

$1$

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

We see that, ${\left(\frac{3}{2}\right)}^{-3}$=${\left(\frac{2}{3}\right)}^3$

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

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

Hence, A is the right answer.