Question

Simplify the expression:
$\left(9^{\frac{1}{2}}\right)\left({81}^{\frac{3}{4}}\right)$

• A. $9$
• B. $27$
• C. $81$
• D. $243$

Answer 1

The correct option is C $81$

We are given with an expression $\left(9^{\frac{1}{2}}\right)\left({81}^{\frac{3}{4}}\right)$

$\underset{–}{Step1:}$

Solving the first bracket:
$(9{)}^{\frac{1}{2}}=(3^2{)}^{\frac{1}{2}}$

$=(3{)}^{2\times \frac{1}{2}}$
$=3^1$
$=3$

$(9{)}^{\frac{1}{2}}=3$

The value of the first bracket, i.e., $(9{)}^{\frac{1}{2}}$ is $3$.

$\underset{–}{Step2:}$

Solving the second bracket:

$(81{)}^{\frac{3}{4}}=(3^4{)}^{\frac{3}{4}}$

$=(3{)}^{4\times \frac{3}{4}}$
$=(3{)}^3$
$=27$

$(81{)}^{\frac{3}{4}}=27$

The value of the second bracket, i.e., $(81{)}^{\frac{3}{4}}$ is $27$.

$\underset{–}{Step3:}$

Multiply the value of first bracket with the value of second bracket:

$\left(9^{\frac{1}{2}}\right)\left({81}^{\frac{3}{4}}\right)=3\times 27$
$=81$

$\left(9^{\frac{1}{2}}\right)\left({81}^{\frac{3}{4}}\right)=81$

The value of the expression $\left(9^{\frac{1}{2}}\right)\left({81}^{\frac{3}{4}}\right)$ is $81$.

Therefore, option (c.) is the correct answer.