Answer:
D. [tex]\frac{4x^{2} \sqrt{29}}{29}[/tex]
Step-by-step explanation:
Given the expression:
[tex]\frac{40x^{2} \sqrt{x^{12} } }{10x^{2} \sqrt{29x^{8} } }[/tex]
divide by the common factor to have;
[tex]\frac{4\sqrt{x^{12} } }{\sqrt{29x^{8} } }[/tex] = [tex]\frac{4(x^{12}) ^{\frac{1}{2} } }{(29x^{8}) ^{\frac{1}{2} } }[/tex]
= [tex]\frac{4x^{6} }{\sqrt{29}x^{4} }[/tex]
= [tex]\frac{4x^{2} }{\sqrt{29} }[/tex]
Rationalize the denominator, we have;
[tex]\frac{4x^{2} }{\sqrt{29} }[/tex] x [tex]\frac{\sqrt{29} }{\sqrt{29} }[/tex]
So that,
[tex]\frac{4x^{2} \sqrt{29} }{29}[/tex]
Thus,
[tex]\frac{40x^{2} \sqrt{x^{12} } }{10x^{2} \sqrt{29x^{8} } }[/tex] = [tex]\frac{4x^{2} \sqrt{29} }{29}[/tex]
The correct option is D.
