How do you simplify m^3sqrtm and write it in exponential form?

Jan 7, 2016

${m}^{\frac{7}{2}}$

Explanation:

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

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

remembering that:

${a}^{p} \cdot {a}^{q} = {a}^{p + q}$

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

$\sqrt[b]{{a}^{n}} = {a}^{\frac{n}{b}}$

alternatively:

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