Question

The value of $3\times (2{)}^{\frac{1}{3}}\times 7\times (6{)}^{\frac{1}{3}}\times 5\times (18{)}^{\frac{1}{3}}$ is

• A. 545
• B. 500
• C. 630
• D. 400

Answer 1

The correct option is C

630

Given $3\times (2{)}^{\frac{1}{3}}\times 7\times (6{)}^{\frac{1}{3}}\times 5\times (18{)}^{\frac{1}{3}}$
$\because (ab{)}^m=a^m\times b^m$
$\Rightarrow (3\times 7\times 5)\times (2\times 6\times 18{)}^{\frac{1}{3}}$
$\Rightarrow 105\times (2\times 6\times 6\times 3{)}^{\frac{1}{3}}$

$\Rightarrow \left[105\right]\times [6^3{]}^{\frac{1}{3}}$

$\because (a^m{)}^n=(a{)}^{m\times n}$
$\Rightarrow \left[105\right]\times [6{]}^{3\times \frac{1}{3}}=105\times 6=630$