Question

The simplified value of (81)^–1/4 × ⁴√81 × (81)^0.2 is​

Answer 1

Given expression: $\[{\left( {81} \right)^{ - \frac{1}{4}}} \times {\left( {81} \right)^{\frac{1}{4}}} \times {\left( {81} \right)^{0.2}}\]$.

Solution:

Simplify the given expression.

$\[{\left( {81} \right)^{ - \frac{1}{4}}} \times {\left( {81} \right)^{\frac{1}{4}}} \times {\left( {81} \right)^{0.2}} = \frac{1}{{{{\left( {81} \right)}^{\frac{1}{4}}}}} \times {\left( {81} \right)^{\frac{1}{4}}} \times {\left( {81} \right)^{0.2}}\]$

                                      $\[\begin{array}{l} = {\left( {81} \right)^{\frac{1}{5}}}\\ = {3^{\frac{4}{5}}}\end{array}\]$

Hence, the simplifivcation of $\[{\left( {81} \right)^{ - \frac{1}{4}}} \times {\left( {81} \right)^{\frac{1}{4}}} \times {\left( {81} \right)^{0.2}}\]$is $\[{3^{\frac{4}{5}}}\]$.