Question

simplify : (3p^2qr^-2/2p^-1q^3)^2
$\div$(2p^3r)^-1 ​

Answer 1

To find :

${ (\dfrac{3 {p}^{2} q {r}^{ - 2} }{2 {p}^{ - 1} {q}^{3} } )}^{2} \div {(2 {p}^{ 3} r ) }^{ - 1}$

Identity used :

$\bullet \: \dfrac{1}{ {a}^{ - m} } = {a}^{m}$

$\bullet \: {a}^{m} \times {a}^{n} = \: {a}^{m + n} \\\\ \bullet \: \dfrac{ {a}^{m} }{ {a}^{n} } \: = \: {a}^{m - n}$

$\bullet \: \: {( {a}^{m} )}^{n} = {a}^{m + n} \\ \bullet \: a \div \dfrac{1}{b} = ab$

Solution :

${ (\dfrac{3 {p}^{2} q {r}^{ - 2} }{2 {p}^{ - 1} {q}^{3}  } )}^{2}   \div  {(2 {p}^{ 3}r ) }^{ - 1}  \\  \\ (  { \dfrac{3}{2} })^{2}  \times ( { {p}^{2 - ( - 1) } \times  {q}^{(1 - 3)}  \times  {r}^{ - 2})  }^{2}  \div  (\dfrac{1}{2 {p}^{ 3}r} ) \\  \\ ( \dfrac{9}{4} ) \times  {( {p}^{3} \times  {q}^{ - 2}   \times  {r}^{ - 2} })^{2}  \times (2 {p}^{ 3} r) \\  \\  \frac{9}{4}  \times  {p}^{3 \times 2}  \times  {q}^{ - 2 \times 2}  \times  {r}^{ - 2 \times 2}  \times (2 {p}^{3}  \times \:r ) \\  \\  \frac{9}{4}  \times  {p}^{6}  \times  {q}^{ - 4}  \times  {r}^{ - 4}  \times 2 \times  {p}^{3}  \times  r  \\  \\  \frac{9 \times 2}{4}  \times  {p}^{6  + ( 3)}  \times  {q}^{ - 4 }  \times  {r}^{ - 4 + 1}  \\  \\  \frac{9}{2}  \times  {p}^{9}  \times  {q}^{ - 4}  \times  {r}^{ - 3}  \\  \\  \frac{9 {p}^{9} }{2{q}^{4} {r}^{3} }$

ANSWER :

$\sf \bold{ \dfrac{9 {p}^{9} }{2{q}^{4}{r}^{3} } }$