Respuesta :
Answer:
[tex]ab^2\sqrt{a}[/tex]
Step-by-step explanation:
We are asked to express [tex]\sqrt{a^3b^4}[/tex] in simplified form.
Using radical rule [tex]\sqrt{mn}=\sqrt{m}\cdot \sqrt{n}[/tex], we will get:
[tex]\sqrt{a^3b^4}=\sqrt{a^3}\cdot\sqrt{b^4}[/tex]
Rewrite [tex]a^3[/tex] as [tex]a^2\cdot a[/tex] and [tex]b^4[/tex] as [tex](b^2)^2[/tex]
[tex]\sqrt{a^3b^4}=\sqrt{a^2\cdot a}\cdot\sqrt{(b^2)^2}[/tex]
Using radical rule [tex]\sqrt{mn}=\sqrt{m}\cdot \sqrt{n}[/tex], we will get:
[tex]\sqrt{a^3b^4}=\sqrt{a^2}\cdot\sqrt{a}\cdot\sqrt{(b^2)^2}[/tex]
Using radical rule [tex]\sqrt[n]{m^n}=m[/tex],we will get:
[tex]\sqrt{a^3b^4}=a\cdot b^2\cdot\sqrt{a}[/tex]
[tex]\sqrt{a^3b^4}=ab^2\cdot\sqrt{a}[/tex]
Therefore, the simplified form of the given expression would be [tex]ab^2\sqrt{a}[/tex].
