Question

$\left[\right(81{)}^{0.25}\times (9{)}^{05}\times (27{)}^{1.5}÷\left(243{)}^{0.5}\right]$ is equal to

• A. $81$
• B. $83$
• C. $85$
• D. $87$

Answer 1

The correct option is A $81$

Given Expression
$[{\left(81\right)}^{0.25}\times {\left(9\right)}^{0.5}\times {\left(27\right)}^{1.5}÷{\left(243\right)}^{0.5}]$
$=[{\left(3^4\right)}^{\frac{1}{4}}\times {\left(3^2\right)}^{\frac{1}{2}}\times {\left(3^3\right)}^{\frac{3}{2}}÷{\left(3^5\right)}^{\frac{1}{2}}]$
$=[\left(3\right)\times \left(3\right)\times {\left(3\right)}^{\frac{9}{2}}÷{\left(3\right)}^{\frac{5}{2}}]$
$=[3\times 3\times 3^{\frac{9-5}{2}}]$
= $3\times 3\times 3^2=81$