Answer:
[tex]a^{\frac{5}{2}} = a^{2}\sqrt{a}[/tex]
Step-by-step explanation:
Given:
Given expression is.
[tex]= a^{\frac{5}{2}}[/tex]
We need to write the given expression in radical form.
Solution:
Rewrite the expression as.
[tex]= a^{\frac{5}{2}}[/tex]
Now we extract power as [tex](a^{m})^{\frac{1}{n} }=a^{\frac{m}{n}}[/tex]
[tex]=(a^{5})^{\frac{1}{2} }[/tex]
Now we write the above expression in radical form and simplify.
[tex]=\sqrt[2]{(a^{5})}[/tex]
[tex]=\sqrt[2]{(a\times a)\times (a\times a)\times a}[/tex]
[tex]=\sqrt[2]{a^{2}\times a^{2}\times a }[/tex]
[tex]= a\times a\times \sqrt[2]{a}[/tex]
[tex]= a^{2}\times \sqrt[2]{a}[/tex]
[tex]a^{\frac{5}{2}} = a^{2}\sqrt{a}[/tex]
Therefore, the radical form of the given expression [tex]a^{\frac{5}{2}} = a^{2}\sqrt{a}[/tex]
