Answer: [tex]2ab^{2} \sqrt[4]{5a}[/tex]
Step-by-step explanation:
Question:
[tex]\sqrt[4]{8a^{3} b}\sqrt[4]{10a^{2} b^{7} }[/tex] =>Because the are the same root let's combine
so all is under the same root
=> Also rearranged so same terms are together
[tex]\sqrt[4]{8(10)a^{3}a^{2} b b^{7} }\\[/tex] => Factorize everything 8=2*2*2
10=2*5
a³=aaa etc.
I grouped variables into 4's so you can
see better.[tex]\sqrt[4]{(2)(2)(2)(2)(5)(aaaa)a(bbbb)(bbbbb)}[/tex]
=> Every set of 4 can come out of the root
because that is what root 4 means [tex]\sqrt[4]{x}[/tex]
So I have 4 2's so i can take a 2 out
I have 4 a's so I can take an"a" out
I have 2 sets of 4 b's so i can take out
2 b's
Everything that does not make a set of 4
stays in the root.
[tex]2abb\sqrt[4]{5a}[/tex] =>combine the 2 b's
[tex]2ab^{2} \sqrt[4]{5a}[/tex]
