How do you multiply 7th root of m raise to 4 times the 14th root of m raise to 9?

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Answer 1 · 2018-06-20T08:34:38

$\Rightarrow {(m)}^{\frac{17}{14}}$ $color(indigo)(=> (m)^(17/14)$

${(\sqrt[7]{m})}^{4} \cdot {(\sqrt[14]{m})}^{9}$ $(root7 (m))^4 * (root14 (m))^9$

![https://revisionmaths.com/advanced-level-maths-revision/pure-maths/algebra/indices]( useruploads.socratic.org )

Applying the theory of indices,

$\Rightarrow ({(m^{4})}^{\frac{1}{7}} \cdot ({(m^{9})}^{\frac{1}{14}})$ $=> ((m^4)^(1/7) * ((m^9)^(1/14))$

$\Rightarrow . {(m)}^{\frac{4}{7}} \cdot {(m)}^{\frac{9}{14}}$ $=>. (m)^(4/7) * (m)^(9/14)$

$\Rightarrow {(m)}^{\frac{4}{7} + \frac{9}{14}}$ $=> (m)^ (4/7 + 9/14)$

$\Rightarrow {(m)}^{\frac{8 + 9}{14}}$ $=> (m)^((8 + 9)/14)$

$\Rightarrow {(m)}^{\frac{17}{14}}$ $color(indigo)(=> (m)^(17/14)$