Question

Simplify: {( -3/4 )³ - (-5/2)³} × 4²​

Answer 1

$\underline\blue{\bold{Given \: Question :- }}$

$\bf \:Simplify: ({( -3/4 )³ - (-5/2)³}) × 4²$

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$\huge \orange{AηsωeR} ✍$

$\underline\blue{\bold{Use \: the \: following \: identities :- }}$

$\begin{gathered}(1)\:{\underline{\boxed{\bf{\blue{a^m\times{a^n}\:=\:a^{m\:+\:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(2)\:{\underline{\boxed{\bf{\purple{\dfrac{a^m}{a^n}\:=\:a^{m\:-\:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(3)\:{\underline{\boxed{\bf{\red{\dfrac{1}{x^n}\:=\:x^{-n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(4)\:{\underline{\boxed{\bf{\color{peru}{(a^m)^n\:=\:a^{m\times{n}}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(5)\:{\underline{\boxed{\bf{\green{( {xy)}^{n} = {x}^{n} \times {y}^{n} }}}}} \\ \end{gathered}$

$\begin{gathered}(6)\:{\underline{\boxed{\bf{\orange{ {(\dfrac{x}{y} )}^{n} = \dfrac{ {x}^{n} }{ {y}^{n} } }}}}} \\ \end{gathered}$

$\begin{gathered}(7)\:{\underline{\boxed{\bf{\green{ {( - x)}^{odd} \:=\: - {(x)}^{odd} }}}}} \\ \end{gathered}$

$\begin{gathered}(8)\:{\underline{\boxed{\bf{\blue{ {( - x)}^{even} \:=\: - {(x)}^{even} }}}}} \\ \end{gathered}$

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$\begin{gathered}\Large{\underline{\bf{\color{purple}CaLcULatIoN,}}} \end{gathered}$

$\begin{gathered}\bf\red{According \: to \: statement}\end{gathered}$

$\bf \:  ⟼ (( {\dfrac{ - 3}{4} )}^{ 3} - ( {\dfrac{ - 5}{2} )}^{3} )\times {4}^{2}$

$\bf \:  ⟼ [ - {(\dfrac{3}{4}) }^{3} + ({\dfrac{5}{2} )}^{3} ] \times {4}^{2}$

$\bf \:  ⟼ [ - \dfrac{ {3}^{3} }{ {4}^{3} } + \dfrac{ {5}^{3} }{ {2}^{3} } ] \times 16$

$\bf \:  ⟼ [ - \dfrac{27}{64} + \dfrac{125}{8} ] \times 16$

$\bf \:  ⟼ [\dfrac{ - 27 + 100}{64} ] \times 16$

$\bf\implies \:\dfrac{963}{4}$

$\large{\boxed{\boxed{\bf\implies \:{(( {\dfrac{ - 3}{4} )}^{ 3} - ( {\dfrac{ - 5}{2} )}^{3} )\times {4}^{2}= \dfrac{963}{4} }}}}$

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