Help - Rationalize the denominator

[mcruz65]

Rationalize the denominator
?(16a^4 b^6 )/?(128a^6 b^6 )
This is what I have done so far. Please let me know if I am doing it correctly.

?16a^2b^6
----------
?128a^6b^6

?16a^2b^6
----------------------
2?2?2?2?2?2?2 a^4 a^2 b^6

?16a^2b^6
---------------------- x 2/2 
2?2?2?2?2?2?2 a^4 a^2 b^6

?32
------
?256a^2

?16?2
------
?256a^2

4?2
------
16a

 

[tutor_joel]

that looks correct, though I can't quite follow your steps. You have one more step to go to reduce the 4/16 to 1/4.

\(\displaystyle \frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\frac{4a^2b^3}{a^3b^3\sqrt{8^2*2}}=\frac{1}{2a\sqrt{2}}=\frac{\sqrt{2}}{4a}\)

 

[mcruz65]

Thank you very much! Yes I caught that last step also.

 

[Denis]

Rationalize the denominator
?(16a^4 b^6 )/?(128a^6 b^6 )
This is what I have done so far. Please let me know if I am doing it correctly.

?16a^2b^6
----------
?128a^6b^6

Check numerator: a^4 or a^2 ? :shock: