8 ^√( 121 ) + 1 2 #160; #160; =( 2 ^ 3 ) #160; ^√( 121 ) + 1 2 #160; #160; =( 2 ^ 3 ) #160; ^√( 121 ) #160; ·( 2 ^ 3 ) ...

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Integers

Solve : 8√12...

Question

Solve : $8^{\sqrt{1} 21 + \frac{1}{2}}$ .

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Solution

$8^{\sqrt{121} + \frac{1}{2}} = {(2^{3})}^{\sqrt{121} + \frac{1}{2}} = {(2^{3})}^{\sqrt{121}} \cdot {(2^{3})}^{\frac{1}{2}} = {(2^{3})}^{11} \cdot {(2^{3})}^{\frac{1}{2}} = 2^{3 \times \frac{23}{2}} = 2^{\frac{69}{2}}$

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[x 1] [\begin{matrix} 1 & 0 \\ - 2 & - 3 \end{matrix}] [\begin{matrix} x \\ 5 \end{matrix}] = 0

[1 2 1] [\begin{matrix} 1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{matrix}] [\begin{matrix} 0 \\ 2 \\ x \end{matrix}] = 0

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12 \frac{1}{2}

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