Question

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Answer 1

Answer:

D. $\frac{4x^{2} \sqrt{29}}{29}$

Step-by-step explanation:

Given the expression:

 $\frac{40x^{2} \sqrt{x^{12} } }{10x^{2} \sqrt{29x^{8} } }$

divide by the common factor to have;

$\frac{4\sqrt{x^{12} } }{\sqrt{29x^{8} } }$ = $\frac{4(x^{12}) ^{\frac{1}{2} } }{(29x^{8}) ^{\frac{1}{2} } }$

        = $\frac{4x^{6} }{\sqrt{29}x^{4} }$

        = $\frac{4x^{2} }{\sqrt{29} }$

Rationalize the denominator, we have;

$\frac{4x^{2} }{\sqrt{29} }$ x $\frac{\sqrt{29} }{\sqrt{29} }$

So that,

$\frac{4x^{2} \sqrt{29} }{29}$

Thus,

$\frac{40x^{2} \sqrt{x^{12} } }{10x^{2} \sqrt{29x^{8} } }$ = $\frac{4x^{2} \sqrt{29} }{29}$

The correct option is D.