Question

Simplify (2x^2)^-3 upon x^5​

Answer 1

$\implies \sf \dfrac{{(2 {x}^{2} )}^{ - 3} }{ {x}^{5} }$

We know that :-

$\red{ \underline {\blue{ \boxed{ \bf \large {(ab)}^{n} = {a}^{n} \times {b}^{n} }}}}$

$\implies \sf \dfrac{{(2 )}^{ - 3} \times{ ({x}^{2} )}^{ - 3} }{ {x}^{5} }$

We know that :-

$\red{ \underline {\blue{ \boxed{ \bf \large ({{a}^{n})}^{m} = {a}^{nm} }}}}$

$\implies \sf \dfrac{{(2 )}^{ - 3} \times{ ({x})^{ - 6} } }{ {x}^{5} }$

We know that :

$\red{ \underline {\blue{ \boxed{ \bf \large \frac{ {a}^{n} }{ {a}^{m} } = {a}^{n - m} }}}}$

$\implies \sf {{(2 )}^{ - 3} \times{ ({x})^{ - 6 - 5} } }$

$\implies \sf {{(2 )}^{ - 3} \times{ ({x})^{ - 11} } }$

We know that :

$\red{ \underline {\blue{ \boxed{ \bf \large {a}^{- m} = \frac{1 }{ {a}^{m} } }}}}$

$\implies \sf \dfrac{1}{{{(2 )}^{ 3} } \times{ ({x})^{ 11} } }$

2³=8

$\implies \sf \dfrac{1}{{8 }{ ({x})^{ 11} } }$

Answer :

$\bf \dfrac{1}{{8 }{ ({x})^{ 11} } }$

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$\large\bf\blue{Additional-Information}$

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

$2) {( {a}^{m})}^{n}  = {a}^{mn}$

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

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

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