Question

if p/q = (32)^-2÷(6/7)^0 , find the value of (p/q)^-3​

Answer 1

$\frac{p}{q} = {32}^{ - 2} \div ({ \frac{6}{7} })^{0} \\ \\ = ( { \frac{1}{32} })^{2} \div 1 \: \: \: \: \: \:---- ( {x}^{0} = 1) \\ \\ = \frac{1}{1024} \times 1 = \frac{1}{1024}$

Then , to find :

$( { \frac{p}{q} })^{ - 3} = {( \frac{1}{1024} )}^{ - 3} \\ \\ = ( {32}^{ - 2} )^{ - 3} = {32}^{6}$

Answer 2

$\blue {\rm \huge \underline{S \large OLUTION \colon}}$



$\sf \dfrac{p}{q} = 32 {}^{ - 2} \div {\bigg( \dfrac{6}{7} \bigg)}^{0} \\ \sf \: \: \: \: \: = {\bigg(\frac{1}{32} \bigg )}^{2} \div 1 \\ \: \: \: \: \: = \sf \frac{1}{1024} \times 1 \\ \: \: \: \: \: = \sf \frac{1}{1024}$

Now, Value of $\sf{ \bigg(\dfrac{p}{q} \bigg)}^{-3}$

$\sf{ \bigg(\dfrac{p}{q} \bigg)}^{-3} = {\bigg(\dfrac{1}{1024} \bigg)}^{ - 3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = {({32}^{ - 2} )} {}^{ - 3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf =32 {}^{6} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf =1073741824$