Question

Simplify this please.
I will mark BRAINLIEST.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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

now we know that :-

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

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

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

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

Now we know that :-

${a}^{ - m} = \frac{1}{ {a}^{m} }$

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

⟹ $( \dfrac{9{p}^{6} }{4{q}^{ 4} {r}^{ 4}} ) \: \times {(2 {p}^{3} r)}$

⟹ $9/2 {(p}^{6+ 3}) {(r}^{1 - 4}) ({q}^{ - 4} )$

⟹ $9/2 {(p}^{9}) {(r}^{ - 3}) ({q}^{ - 4} )$

Answer :-

$(9/2) {(p}^{9}) {(r}^{ - 3}) ({q}^{ - 4} )$

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CONCEPT :-

$1)a^m \times a^n= {a}^{(m + n)}$

$2) {( {a}^{m})}^{n}  = {a}^{mn}$

$3) {ab}^{n} = {a}^{n} {b}^{n}$

$4) \frac{ {(a)}^{m} }{ {(a)}^{n} } = {a}^{m - n}$

$5) {a}^{ - b} = \frac{1}{ {a}^{b} }$

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