Question

Enter the correct answer in the box. IF x≠0, what is the sum of 4 v^3 x^10 + 5x^3 ^3

Answer 1

Answer: $14*\sqrt[3]{x^{10}}$

Step-by-step explanation:

First, let's remember the rules:

$x^{1/n} = \sqrt[n]{x}$

such that:

$\sqrt[n]{x^m} = x^{m/n}$

$(x^a)^b = x^{a*b}$

$x^a*x^b = x^{a + b}$

Now we have the equation:

$4*\sqrt[3]{x^{10}} + 5*x^3*\sqrt[3]{8*x}$

First, let's rewrite the roots as we saw above:

$4*x^{10/3} + 5*x^3*\sqrt[3]{8}*x^{1/3} = 4*x^{10/3} + 5*\sqrt[3]{8}*x^{3 + 1/3}$

We also know that: $\sqrt[3]{8} = 2$

and that:  $3 + 1/3 = 9/3 + 1/3 = 10/3$

Replacing those two things in our equation, we get:

$4*x^{10/3} + 5*\sqrt[3]{8}*x^{3 + 1/3} = 4*x^{10/3} + 5*2*x^{10/3} = (4 + 5*2)*x^{10/3}$

$(4 + 10)*x^{10/3} = 14*\sqrt[3]{x^{10}}$

Where in the final step, I returned to the cubic root form.