Question

Evaluate (3)^1/6 × (3)^-2/3

Answer 1

39918656718818881883

Answer 2

`(1)/(√(3))`

Explanation:

Evaluate:
`3^{(1)/(6)} * 3^{-(2)/(3)}`

Apply exponent rule:
`a^b * a^c=a^(b+c)`

`\begin{aligned} \implies 3^{(1)/(6)} * 3^{-(2)/(3)}&=3^{(1)/(6)-(2)/(3)}\\ &=3^{-(1)/(2)\end{aligned}`

Apply exponent rule:
`a^(-n)=(1)/(a^n)`

`\implies 3^{-(1)/(2)}=\frac{1}{3^{(1)/(2)}}=(1)/(√(3))`