Answer: [tex]14*\sqrt[3]{x^{10}}[/tex]
Step-by-step explanation:
First, let's remember the rules:
[tex]x^{1/n} = \sqrt[n]{x}[/tex]
such that:
[tex]\sqrt[n]{x^m} = x^{m/n}[/tex]
[tex](x^a)^b = x^{a*b}[/tex]
[tex]x^a*x^b = x^{a + b}[/tex]
Now we have the equation:
[tex]4*\sqrt[3]{x^{10}} + 5*x^3*\sqrt[3]{8*x}[/tex]
First, let's rewrite the roots as we saw above:
[tex]4*x^{10/3} + 5*x^3*\sqrt[3]{8}*x^{1/3} = 4*x^{10/3} + 5*\sqrt[3]{8}*x^{3 + 1/3}[/tex]
We also know that: [tex]\sqrt[3]{8} = 2[/tex]
and that: [tex]3 + 1/3 = 9/3 + 1/3 = 10/3[/tex]
Replacing those two things in our equation, we get:
[tex]4*x^{10/3} + 5*\sqrt[3]{8}*x^{3 + 1/3} = 4*x^{10/3} + 5*2*x^{10/3} = (4 + 5*2)*x^{10/3}[/tex]
[tex](4 + 10)*x^{10/3} = 14*\sqrt[3]{x^{10}}[/tex]
Where in the final step, I returned to the cubic root form.
