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C1 Indices question help

(6^1/4*36^1/8)∕√6

The answer is 1 but I don't understand how to get there.

Sorry I know there's a way of displaying this in a clearer way but I have no idea how. Anyways thanks in advance.
(edited 7 years ago)
Reply 1
614×36186 \frac{6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}{\sqrt 6}
You can do this using latex as this site allows latex preview. Have a look at this site. https://www.codecogs.com/latex/eqneditor.php
Reply 2
Original post by asif144
614×36186 \frac{6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}{\sqrt 6}
You can do this using latex as this site allows latex preview. Have a look at this site. https://www.codecogs.com/latex/eqneditor.php


Aah thank you. That's useful for future reference. Any idea how to solve it though?
Original post by b_lythe
Aah thank you. That's useful for future reference. Any idea how to solve it though?


36 is the same as 6^2, from there, you should be able to see that 36^1/8 is the same as (6^2)^1/8, which simplifies nicely to give 6^1/4. You can do it from here if you remember that 6^1/2 is the same as root6
Reply 4
Original post by Ishan_2000
36 is the same as 6^2, from there, you should be able to see that 36^1/8 is the same as (6^2)^1/8, which simplifies nicely to give 6^1/4. You can do it from here if you remember that 6^1/2 is the same as root6


Thank you!
Reply 5
Here's the full worked process

[latex ] {\frac{6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}{\sqrt 6}}

=614×3618÷6 ={6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}\div{\sqrt 6}

=614×3618÷612 ={6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}\div{6^\frac{1}{2}}

=628×3618÷648 ={6^{\frac{2}{8}}\times 36^{\frac{1}{8}}}\div{6^\frac{4}{8}}

=628×(62)18÷648 ={6^{\frac{2}{8}}\times{(6^2)}^{\frac{1}{8}}}\div{6^\frac{4}{8}}

=628×628÷648 ={6^{\frac{2}{8}}\times 6^{\frac{2}{8}}}\div{6^\frac{4}{8}}

=648÷648 ={6^{\frac{4}{8}}}\div{6^\frac{4}{8}}

=60 ={6^0}

=1 ={1}

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