Question

the simplified value of (81)^-1/4 * 4√81* (81)^0.2​

Answer 1

Answer:

The correct answer is 9

Step-by-step explanation:

(81n-1/4 (81)1/4"(81o.5

(81)(-14+1/4+0.5) as base is equal we can add

the exponent

(81) 0.5 as -1/4 and 1/4 in the power gets

canceled on addition

(sqrt 81) =9

Answer 2

Given,

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

Solution,

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

$\[ = {\left( {81} \right)^{\left( {\frac{{ - 1}}{4}} \right)}} \times 4{\left( {81} \right)^{\frac{1}{2}}} \times {\left( {81} \right)^{0.2}}\]$

$\[ = {\left( {81} \right)^{\left( {\frac{{ - 1}}{4}} \right)}} \times 4{\left( {81} \right)^{\frac{1}{2}}} \times {\left( {81} \right)^{\frac{1}{5}}}\]$

$\[ = 4 \times {\left( {81} \right)^{\left( {\frac{{ - 1}}{4} + \frac{1}{2} + \frac{1}{5}} \right)}}\]$

$\[ = 4 \times {\left( {81} \right)^{\left( {\frac{9}{{20}}} \right)}}\]$

$\[ = 4 \times {\left( 9 \right)^{\left( {\frac{9}{{10}}} \right)}}\]$

$\[ = 4 \times \sqrt[{10}]{{\left( {{9^9}} \right)}}\]$

$\[ = 4 \times 7.224\]$

$\[ = 28.9\]$

Hence the value is $\[28.9\]$