Question

For $a=27,b=8,m=\frac{1}{3}$ verify $(ab{)}^m=a^m{b}^m$

Answer 1

$a=27,b=8,m=\frac{1}{3}$

Now,

${\left(ab\right)}^m=a^m{b}^m$

${(27\times 8)}^{\frac{1}{3}}={\left(27\right)}^{\frac{1}{3}}\times {\left(8\right)}^{\frac{1}{3}}$

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

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

${\left(6\right)}^{3\times \frac{1}{3}}=2\times 3$

$6=6$

L.H.S. $=$ R.H.S.

Hence verified.