Question

Find the value of
${81}^{\frac{1}{3}}\times {576}^{\frac{1}{3}}$

• A. $36$
  
• B. $40$
  
• C. $26$
  
• D. $30$
  

Answer 1

The correct option is A $36$


${81}^{\frac{1}{3}}\times {576}^{\frac{1}{3}}=(81\times 576{)}^{\frac{1}{3}}$
$={\{(3^2\times 3^2)\times (4^3\times 3^2)\}}^{1/3}$
$={(3^{2+2+2}\times 4^3)}^{\frac{1}{3}}$
$=(3^6\times 4^3{)}^{\frac{1}{3}}$
$=(3^6{)}^{\frac{1}{3}}\times (4^3{)}^{\frac{1}{3}}$ $[Using:(x\times y{)}^a=x^a\times y^a]$
$=3^{6\times \frac{1}{3}}\times 4^{3\times \frac{1}{3}}$ $[Using:(x^a{)}^b=x^{ab}]$
$=3^2\times 4$
$=9\times 4$
$=36$