Question

√m . ∛(m^2 ) . ∜(m^3 ) =

Answer 1

Respuesta:      $m^{\frac{23}{12}}$

Explicación paso a paso:

$\sqrt{m}\sqrt[3]{m^2}\sqrt[4]{m^3}$

$\sqrt[3]{m^2}:\quad m^{\frac{2}{3}}$

$=\sqrt{m}m^{\frac{2}{3}}\sqrt[4]{m^3}$

$\sqrt[4]{m^3}:\quad m^{\frac{3}{4}}$

$=\sqrt{m}m^{\frac{2}{3}}m^{\frac{3}{4}}$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$m^{\frac{2}{3}}m^{\frac{3}{4}}=\:m^{\frac{2}{3}+\frac{3}{4}}$

$=\sqrt{m}m^{\frac{2}{3}+\frac{3}{4}}$

$m^{\frac{2}{3}+\frac{3}{4}}=m^{\frac{17}{12}}$

$=m^{\frac{17}{12}}\sqrt{m}$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$m^{\frac{17}{12}}\sqrt{m}=\:m^{\frac{17}{12}}m^{\frac{1}{2}}=\:m^{\frac{17}{12}+\frac{1}{2}}$

$=m^{\frac{17}{12}+\frac{1}{2}}$

$\mathrm{Simplificar}\:\frac{17}{12}+\frac{1}{2}\:\mathrm{en\:una\:fraccion}:\quad \frac{23}{12}$

$=m^{\frac{23}{12}}$

Answer 2

Respuesta:

$m \sqrt[12]{ {m}^{11} }$

Explicación paso a paso:

$\sqrt{m} ( \sqrt[3]{ {m}^{2} } )( \sqrt[4]{ {m}^{3} } ) = \sqrt[12]{ {m}^{6} } ( \sqrt[12]{ {m}^{8} } )( \sqrt[12]{ {m}^{9} } )$

$\sqrt[12]{ {m}^{6 + 8 + 9} }$

$\sqrt[12]{ {m}^{23} } = m \sqrt[12]{ {m}^{11} }$