How do you simplify $(root3(6)*root4(6))^12$ ?

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Answer 1 · 2017-03-19T20:33:57

$(root3(6)*root(4)6)^12=6^7=279936$

We need the rules:

Using $color(red)star$ , we see that:

$(root3(6)*root(4)6)^12=(6^(1/3)*6^(1/4))^12$

Now using $color(green)star$ , this becomes:

$(6^(1/3)*6^(1/4))^12=(6^(1/3+1/4))^12$

Note that $1/3+1/4=4/12+3/12=7/12$ .

$(6^(1/3+1/4))^12=(6^(7/12))^12$

Now using $color(blue)star$ , we multiply the exponents:

$(6^(7/12))^12=6^(7/12xx12)$

And we see that $7/12xx12=7$ :

$6^(7/12xx12)=6^7$

All of which we did without a calculator! For an expanded value, we could plug in $6^7$ into a calculator to see that $6^7=279936$ .

How do you simplify (root3(6)*root4(6))^12(root3(6)*root4(6))^12?