C1 Indices question help

b_lythe

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(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.

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asif144

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$\frac{6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}{\sqrt 6}$
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

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b_lythe

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(Original post by asif144)
$\frac{6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}{\sqrt 6}$
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?

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Ishan_2000

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(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

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b_lythe

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(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!

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Jpnock

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Here's the full worked process

${\frac{6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}{\sqrt 6}}$

$={6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}\div{\sqrt 6}$

$={6^{\frac{1}{4}}\times 36^{\frac{1}{8}}}\div{6^\frac{1}{2}}$

$={6^{\frac{2}{8}}\times 36^{\frac{1}{8}}}\div{6^\frac{4}{8}}$

$={6^{\frac{2}{8}}\times{(6^2)}^{\frac{1}{8}}}\div{6^\frac{4}{8}}$

$={6^{\frac{2}{8}}\times 6^{\frac{2}{8}}}\div{6^\frac{4}{8}}$

$={6^{\frac{4}{8}}}\div{6^\frac{4}{8}}$

$={6^0}$

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