Question

simply
$\sqrt[4]{12} \times \sqrt[7]{6}$
​

Answer 1

$\sqrt[4]{12} \times \sqrt[7]{6}$

tex] \sqrt[4]{2×2×3} \times \sqrt[7]{2×3} [/tex]

Answer 2

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step-by-step explanation :

$\sqrt[4]{12} \times \sqrt[7]{6}$

Now,

we know that,

$\sqrt[n]{a}$ = ${a}^{1/n}$

so,

simplifying according to this formula,

we get,

= ${12}^{1/4}$× ${6}^{1/7}$

= ${(2×2×3)}^{1/4}$ × ${(2×3)}^{1/7}$

Now,

we know that,

${(ab)}^{m}$ = ${a}^{m}$${b}^{m}$

so,

putting the above values on this formula,

we get,

= ${2}^{1/4}$ × ${2}^{1/4}$× ${3}^{1/4}$ × ${2}^{1/7}$ × ${3}^{1/7}$

Now,

we know that,

${a}^{p}$×${a}^{q}$ = ${a}^{(p+q)}$

so,

putting the values on this formula,

we get,

= ${3}^{(1/4+1/7)}$ × ${2}^{(1/4+1/4+1/7)}$

Simplifying we get,

= ${3}^{11/28}$ × ${2}^{18/28}$

= ${3}^{11/28}$ × ${2}^{9/14}$