Question

Find the value of x^2, if x^-3 -0.001=0

Answer 1

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{ {x}^{ - 3} - 0.001 = 0} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\tt{ {x}^{2} }  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

$\tt \ \: :  ⟼ {x}^{ - 3} - 0.001 = 0$

$\tt \ \: :  ⟼ {x}^{ - 3} = 0.001$

$\tt \ \: :  ⟼ {x}^{ - 3} = \dfrac{1}{1000}$

$\tt \ \: :  ⟼ {x}^{ - 3} = \dfrac{1}{ {(10)}^{ - 3} }$

$\tt \ \: :  ⟼ {x}^{ - 3} = {(10)}^{ - 3}$

$\tt\implies \:x = 10$

$\tt \ \: :  ⟼ Now, \: {x}^{2} = {(10)}^{2} = 100$

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Additional Information

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

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

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

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

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

$\begin{gathered}(6)\:{\underline{\boxed{\bf{\green{ {if \: x}^{m} = {x}^{n} \tt\implies \: \: m \: = \: n}}}}} \\ \end{gathered}$