If $3^{x} - 3^{x - 1} = 18$ , then $x^{x} = ?$

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Solution

Find the value of of the given expression
Given $3^{x} - 3^{x - 1} = 18$
$\begin{array}{rcl} ∴ 3^{x} - 3^{x - 1} & = & 18 \\ \Rightarrow & 3^{x} - \frac{3^{x}}{3} = 18 \\ \Rightarrow & 3^{x} \times (1 - \frac{1}{3}) = 18 \\ \Rightarrow & 3^{x} \times \frac{2}{3} = 18 \\ \Rightarrow & 3^{x} = 27 \\ \Rightarrow & 3^{x} = 3^{3} \\ \Rightarrow & x = 3 \\ \Rightarrow & x^{x} = 3^{3} = 27 \end{array}$
Hence the answer is $27$

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