Question

Evaluate (3)^1/6 × (3)^-2/3

Answer 1

39918656718818881883

Answer 2

Answer:

$\dfrac{1}{\sqrt{3}}$

Step-by-step explanation:

Evaluate:  $3^{\frac{1}{6}} \times 3^{-\frac{2}{3}}$

Apply exponent rule:  $a^b \times a^c=a^{b+c}$

$\begin{aligned} \implies 3^{\frac{1}{6}} \times 3^{-\frac{2}{3}}&=3^{\frac{1}{6}-\frac{2}{3}}\\ &=3^{-\frac{1}{2}\end{aligned}$

Apply exponent rule:  $a^{-n}=\dfrac{1}{a^n}$

$\implies 3^{-\frac{1}{2}}=\dfrac{1}{3^{\frac{1}{2}}}=\dfrac{1}{\sqrt{3}}$