(9(27(81(243^(1/3))^(1/3))^(1/3))^(1/3)= 3^((x+2)/x)

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${lim}_{x \to 3} (\frac{1}{x - 3} - \frac{3}{x^{2} - 3 x})$

Q. The value of

lim x \to \infty \frac{2 {(x)}^{1 / 2} + 3 {(x)}^{1 / 3} + \dots + n {(x)}^{1 / n}}{{(2 x - 3)}^{1 / 2} + {(2 x - 3)}^{1 / 3} + \dots + {(2 x - 3)}^{1 / n}}

Q. Evaluate

3 \times 3^{1 / 2} \times 3^{1 / 4} \times 3^{1 / 8} \times

...to

\infty

Q. Prove that

3^{\frac{1}{2}} \times 3^{\frac{1}{4}} \times 3^{\frac{1}{8}} . . . . . = 3

Which of the following are not true?

i) $3^{(\frac{1}{3})}$ = $\sqrt{3^{- 3}}$
ii) $3^{(\frac{1}{2})}$ = $\sqrt{3^{2}}$
iii) $3^{- 2}$ = $\sqrt{3}$
iv) $3^{(\frac{1}{2})}$ = $\sqrt{3}$

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