Question

$$\alpha \sqrt{ \alpha }$$

Answer

$$a^3*l*p*h*sqrt(l*p*h)$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{a}^{2}lph\sqrt{{a}^{2}lph}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[{a}^{2}lph\sqrt{{a}^{2}}\sqrt{lph}\]
Simplify  \(\sqrt{{a}^{2}}\)  to  \(a\).
\[{a}^{2}lpha\sqrt{lph}\]
Regroup terms.
\[{a}^{2}alph\sqrt{lph}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{a}^{2+1}lph\sqrt{lph}\]
Simplify  \(2+1\)  to  \(3\).
\[{a}^{3}lph\sqrt{lph}\]