1.
16^(-0.75)=(2⁴)^(-³/₄)=2⁻³ = 1/8=0.125
2.
4^(¹/₃ - ⁵/₆) =(2²)^( - ³/₆)= (2²)^(- ¹/₂)=2⁻¹ = 1/2=0.5
3.
3^(2-3√3) * 3^(3√3)=3^(2-3√3+3√3)=3²=9
4.
2^(2(3+√2)+1-√2-4-√2)=2^(6+2√2+1-√2-4-√2)=2³=8
5.
a^(√2 +1-√2)=a
6.
b^(¹/₁₂) *(⁴√b⁵)^(¹/₃)=b^(¹/₁₂) * b^(⁵/₁₂)=b^(⁶/₁₂)=b^(¹/₂)=√b
7.
((ab⁻²)^(¹/₃)+(ab)^(-¹/₆))(ab⁴)^(¹/₆)=
=a^(¹/₃)b^(-²/₃)*a^(¹/₆)b^(²/₃)+a^(-¹/₆)b^(-¹/₆)*a^(¹/₆)b^(²/₃)=
=a^(¹/₃ + ¹/₆)b(-²/₃ + ²/₃) + a^(-¹/₆ + ¹/₆)b^(-¹/₆ + ²/₃)=
=a^(³/₆)b⁰ + a⁰b^(³/₆)=a^(¹/₂)+b^(¹/₂)=√a + √b