Question

if p/q = (3/4)^18 ÷ (3/6)^16 find a value of (p/q)^2​

Answer 1

Step-by-step explanation:

$\frac{p}{q}$ = $(\frac{3}{4})^{18}$÷$(\frac{3}{6})^{16}$

$\frac{p}{q}$ = $(\frac{3}{4})^{18}$×$(\frac{6}{3})^{16}$

$\frac{p}{q}$ = $(\frac{3}{2×2})^{18}$×$(\frac{3×2}{3})^{16}$

$\frac{p}{q}$ = $\frac{3^{18}}{(2²)^{18}}$×${2^{16}}$

$\frac{p}{q}$ = $\frac{3^{18}}{2^{36}}$×${2^{16}}$

$\frac{p}{q}$ = $\frac{3^{18}}{2^{20}}$

Now, squaring both sides

$(\frac{p}{q})^2$ = $(\frac{3^{18}}{2^{20}})^2$

$(\frac{p}{q})^2$ = $\frac{3^{36}}{2^{40}}$