Question

I NEED HELP Pleaseeeeee

Answer 1

`9^{(1)/(2)}\implies \sqrt[2]{9^1}\implies \text{\LARGE 3} \\\\[-0.35em] ~\dotfill\\\\ 3^{(1)/(2)}\cdot 3^{(1)/(2)}\implies 3^{(1)/(2)+(1)/(2)}\implies 3^{(1)/(4)}\implies \sqrt[4]{3^1} \\\\\\ \sqrt[6]{27}\implies \sqrt[6]{3^3}\implies 3^{(3)/(6)}\implies 3^{(1)/(2)}\implies √(3) \\\\\\ 27^{(1)/(3)}\cdot 3^{(1)/(2)}\implies (3^3)^{(1)/(3)}\cdot 3^{(1)/(2)}\implies 3\cdot 3^{(1)/(2)}\implies 3^{(3)/(2)}\implies \sqrt[2]{3^3}`

`81^{(1)/(2)}\cdot 81^{(1)/(2)}\implies (3^4)^{(1)/(2)}\cdot (3^4)^{(1)/(2)}\implies 3^2\cdot 3^2\implies 81 \\\\\\ 729^{(1)/(6)}\implies (3^6)^{(1)/(6)}\implies \text{\LARGE 3 ~ \checkmark}`

`81^{(1)/(3)}\cdot 81^{(1)/(3)}\implies (3^4)^{(1)/(3)}\cdot (3^4)^{(1)/(3)}\implies 3^{(4)/(3)}\cdot 3^{(4)/(3)}\implies 3^{(8)/(3)}\implies \sqrt[3]{3^8} \\\\\\ 81^{(1)/(4)}\cdot 81^{(1)/(4)}\implies (3^4)^{(1)/(4)}\cdot (3^4)^{(1)/(4)}\implies 3\cdot 3\implies 9`