Question

The value of $(343{)}^{\frac{1}{3}}\times (64{)}^{\frac{1}{3}}$ is

• A. 28
• B. - 28
• C. 18
• D. - 18

Answer 1

The correct option is A

28

Given : $(343{)}^{\frac{1}{3}}\times (64{)}^{\frac{1}{3}}$ is
$=(7\times 7\times 7{)}^{\frac{1}{3}}\times (4\times 4\times 4{)}^{\frac{1}{3}}$

$\because a^m\times b^m=(ab{)}^m$

$=(7\times 7\times 7\times 4\times 4\times 4{)}^{\frac{1}{3}}$

$=(7^3\times 4^3{)}^{\frac{1}{3}}$

$=\left(\right(7\times 4{)}^3{)}^{\frac{1}{3}}$

$\because (a^m{)}^n=(a{)}^{m\times n}$

$=(7\times 4{)}^{3\times \frac{1}{3}}$

$=28$