Question

Evaluate the question​

Answer 1

Question :-

$\bf \:Evaluate \: {27}^{\dfrac{ - 1}{3} } \times {27}^{\dfrac{ - 1}{3} } \times ( {27}^{\dfrac{ 1}{3} } - {27}^{\dfrac{ 2}{3} } )$

$\huge \orange{AηsωeR} ✍$

$\large \red{\bf \: ⟼ Identity \: used :- } ✍$

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

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

$\begin{gathered}(3)\:{\underline{\boxed{\bf{\orange{\dfrac{1}{x^n}\:=\:x^{-n}\:}}}}} \\ \end{gathered}</p><p>$

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

$\begin{gathered}(5)\:{\underline{\boxed{\bf{\color{red}{(a^0)\:=\:1\:}}}}} \\ \end{gathered}$

$\large \red{\bf \: ⟼ Solution :- } ✍$

$\bf \:{27}^{\dfrac{ - 1}{3} } \times {27}^{\dfrac{ - 1}{3} } \times ( {27}^{\dfrac{ 1}{3} } - {27}^{\dfrac{ 2}{3} } )$

$\bf \: ⟼ {27}^{\dfrac{ - 1}{3} + \dfrac{ - 1}{3} } ( {27}^{\dfrac{ 1}{3} } - {27}^{\dfrac{ 2}{3} })$

$\bf \: ⟼ {27}^{\dfrac{ - 2}{3} }( {27}^{\dfrac{ 1}{3} } - {27}^{\dfrac{ 2}{3} })$

$\bf \: ⟼ {27}^{\dfrac{ - 2}{3} } \times {27}^{\dfrac{ 1}{3} } - {27}^{\dfrac{ - 2}{3} } \times {27}^{\dfrac{ 2}{3} }$

$\bf \: ⟼ {27}^{\dfrac{ - 2}{3} + \dfrac{1}{3} } - {27}^{\dfrac{ - 2}{3} + \dfrac{2}{3} }$

$\bf \: ⟼ {27}^{\dfrac{ - 1}{3} } - {27}^{0}$

$\bf \: ⟼ {3}^{3 \times \dfrac{ - 1}{3} } - 1$

$\bf \: ⟼ {3}^{ - 1} - 1$

$\bf \: ⟼ \dfrac{1}{3} - 1$

$\bf \: ⟼ \dfrac{1 - 3}{3}$

$\bf \: ⟼ - \dfrac{2}{3}$

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