Question

reduce the index as small as possible if you can!

picture on side

Answer 1

\[\sqrt[4]{121a^6x^4}\]

Answer 2

ok so are you able to pull anything out?

Answer 3

what do you mean?

Answer 4

so is anything under the radical able to have a fourth root taken?

Answer 5

You're looking for something underneath the radical sign that you can take the fourth root of. For example, you have x^4 underneath the radical. So, if we take the fourth root of this, we can pull it out in front. The fourth root of x^4 is just x (since x^4 = x^4) so we can put the x in front and eliminate the x^4:
\[x \sqrt[4]{121a^6}\]Now, try doing the same thing with the other factors underneath the radical.

Answer 6

^agreed. Don't forget the \({+}{-}\) before the x because it can be positive or negative

Answer 7

\[(121) \frac{ 1 }{ 4 }a \frac{ 4 }{ 6 }x \frac{ 4 }{ 4 } reduced \to (11)\frac{ 1 }{ 4 } a \]

Answer 8

\[\frac{ 4 }{ 6 } x \frac{ 4 }{ 4}\]

Answer 9

not quite, so remember after vinnv's we were left with \[+/-~~x(121a^6)^{\frac{1}{4}}\]
the exponent is another way to write the radical

Answer 10

I don't believe 121 has any factors that are perfect "fourth powers," so we'll have to either leave it under the radical or approximate the fourth root of 121. Lets look at the a^6 though. Finding the fourth root, as mentioned above, is the same as raising to the 1/4 power. So, we can divide the exponent by 4. So the fourth root of a^6 is equal to a^(6/4) or a^(3/2). So we can pull that out in front to get:
\[\pm xa^{3/2}\sqrt[4]{121}\]

Answer 11

I concur but I would prefer you to not give the answer here, so our questioner asks for himself