Question

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

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

$\because a^m\times b^m=(ab{)}^m$
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$=(7\times 7\times 7\times 4\times 4\times 4{)}^{\frac{1}{3}}$

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

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

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

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

$=28$\
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\left[1.5\right]$