Question

The simplified form of $\sqrt[4]{4(81{)}^{-2}}$ is:

• A. $\frac{1}{81}$
• B. $\frac{1}{9}$
• C. $\frac{1}{3}$
• D. $9$

Answer 1

The correct option is B $\frac{1}{9}$

We can use $a^{-n}=\frac{1}{a^n}$.

$\sqrt[4]{4{\left(81\right)}^{-2}}=\sqrt[4]{4\frac{1}{{\left(81\right)}^2}}$

$=\sqrt[4]{4\frac{1}{81\times 81}}$

$=\sqrt[4]{4\frac{1}{(3\times 3\times 3\times 3)\times (3\times 3\times 3\times 3)}}$

$=\sqrt[4]{4\frac{1}{(3\times 3)(3\times 3)(3\times 3)(3\times 3)}}$

$=\frac{1}{(3\times 3)}=\frac{1}{9}$