How do you simplify $m^{3} \sqrt{m}$ $m^3sqrtm$ and write it in exponential form?

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How do you simplify $m^{3} \sqrt{m}$ $m^3sqrtm$ and write it in exponential form?

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Answer 1 · 2016-01-07T22:41:41

$m^{\frac{7}{2}}$ $m^(7/2)$

Explanation:

We can move $m^{3}$ $m^3$ under $\sqrt{}$ $sqrt()$

$m^{3} \sqrt{m} = \sqrt{{(m^{3})}^{2} \cdot m} = \sqrt{m^{6} \cdot m} = \sqrt{m^{7}} = m^{\frac{7}{2}}$ $m^3sqrt(m)=sqrt((m^3)^2*m)=sqrt(m^6*m)=sqrt(m^7)=m^(7/2)$

remembering that:

$a^{p} \cdot a^{q} = a^{p + q}$ $a^p*a^q=a^(p+q)$

${(a^{p})}^{q} = a^{p \cdot q}$ $(a^p)^q=a^(p*q)$

$\sqrt[b]{a^{n}} = a^{\frac{n}{b}}$ $root(b)(a^n)=a^(n/b)$

alternatively:

$m^{3} \sqrt{m} = m^{3} m^{\frac{1}{2}} = m^{3 + \frac{1}{2}} = m^{\frac{3 \cdot 2 + 1}{2}} = m^{\frac{6 + 1}{2}} = m^{\frac{7}{2}}$ $m^3sqrt(m)=m^3m^(1/2)=m^(3+1/2)=m^((3*2+1)/2)=m^((6+1)/2)=m^(7/2)$

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How do you simplify $m^{3} \sqrt{m}$ $m^3sqrtm$ and write it in exponential form?

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How do you simplify $m^{3} \sqrt{m}$ $m^3sqrtm$ and write it in exponential form?