How do you simplify #(27 ^(1/12) * 27 ^(-5/12))^-2#?
1 Answer
Explanation:
Keep in mind that
#(a^b)^c = a^(b*c)#
and
#a^b*a^c = a^(b+c)#
and
#a^(b/c)=root(c)(a^b)#
and
#root(b)(a^b) = a#
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Use the first concept above and apply it to the first step.
#(27^(1/12)*27^(-5/12))^-2#
#(27^(1/12*-2/1) * 27^(-5/12*-2/1))#
#(27^(-2/12) * 27^(10/12))#
Simplify the fractions that are serving as exponents.
#(27^(-1/6)*27^(5/6))#
Now apply the second concept mentioned above. Simplify the fractions again.
#(27^(-1/6+5/6))#
#27^(4/6)#
#27^(2/3)#
Use the third concept noted at the top.
#root(3)(27^2)#
Calculate the the value inside the radicand and rewrite.
#root(3)(729)#
Find the cube root by rewriting the radicand again. Follow the fourth concept after.
#root(3)(9^3)#
#9#
