Answer:
[tex]2a^3(\sqrt[4]{9b^3} )[/tex]
Step-by-step explanation:
Given:
[tex]\sqrt[4]{144a^{12}b^3}[/tex]
144 as a product of its prime factors is [tex]2^4\times 3^2[/tex]
Now, [tex]a^{12}[/tex] can be written as [tex](a^3)^4[/tex] [tex](\because (a^m)^n=a^{m\times n})[/tex]
We know that, [tex]\sqrt[4]{a^4} =a[/tex]
Hence, the given expression becomes,
[tex]\sqrt[4]{2^4\times 3^2\times (a^3)^4\times b^3} \\=2a^3(\sqrt[4]{3^2\times b^3}\\ =2a^3(\sqrt[4]{9b^3})[/tex]
