Evaluate 111. 111. 1−1=01 - 1 = 01−1=0. 14\dfrac{1}{4}41. 127\dfrac{1}{27}271. 110+1100=0.11\dfrac{1}{10} + \dfrac{1}{100} = 0.11101+1001=0.11. Simplify x5+(−3)=x2x^{5 + (-3)} = x^2x5+(−3)=x2. y2−(−4)=y6y^{2 - (-4)} = y^6y2−(−4)=y6. a−2×3=a−6=1a6a^{-2 \times 3} = a^{-6} = \dfrac{1}{a^6}a−2×3=a−6=a61. (2m)−2=1(2m)2=14m2(2m)^{-2} = \dfrac{1}{(2m)^2} = \dfrac{1}{4m^2}(2m)−2=(2m)21=4m21. 3a3−7=3a−4=3a43a^{3-7} = 3a^{-4} = \dfrac{3}{a^4}3a3−7=3a−4=a43. 4(1)+1=54(1) + 1 = 54(1)+1=5. Mixed algebraic 84⋅p5−2q−3−(−1)=2p3q−2=2p3q2\dfrac{8}{4} \cdot p^{5-2} q^{-3-(-1)} = 2p^3 q^{-2} = \dfrac{2p^3}{q^2}48⋅p5−2q−3−(−1)=2p3q−2=q22p3. 9a−2b4=9b4a29a^{-2}b^4 = \dfrac{9b^4}{a^2}9a−2b4=a29b4. 4x64x−1=x6−(−1)=x7\dfrac{4x^6}{4x^{-1}} = x^{6 - (-1)} = x^74x−14x6=x6−(−1)=x7. 1a−5×a−3=a5×a−3=a2\dfrac{1}{a^{-5}} \times a^{-3} = a^5 \times a^{-3} = a^2a−51×a−3=a5×a−3=a2. x−2x−4⋅y3y−1=x−2−(−4)y3−(−1)=x2y4\dfrac{x^{-2}}{x^{-4}} \cdot \dfrac{y^3}{y^{-1}} = x^{-2 - (-4)} y^{3 - (-1)} = x^2 y^4x−4x−2⋅y−1y3=x−2−(−4)y3−(−1)=x2y4. ✓\checkmark✓ Challenge ax−y=axay=82=4a^{x - y} = \dfrac{a^x}{a^y} = \dfrac{8}{2} = 4ax−y=ayax=28=4. 132=2−5\dfrac{1}{32} = 2^{-5}321=2−5, so n=−5n = -5n=−5. (2a−3b2)−2=(b22a−3)2=b44a−6=a6b44\left(\dfrac{2a^{-3}}{b^2}\right)^{-2} = \left(\dfrac{b^2}{2a^{-3}}\right)^2 = \dfrac{b^4}{4a^{-6}} = \dfrac{a^6 b^4}{4}(b22a−3)−2=(2a−3b2)2=4a−6b4=4a6b4. With x=4x = 4x=4: x−1=0.25x^{-1} = 0.25x−1=0.25, x0=1x^0 = 1x0=1, x1/2=2x^{1/2} = 2x1/2=2, x3=64x^3 = 64x3=64. Order: x−1<x0<x1/2<x3x^{-1} < x^0 < x^{1/2} < x^3x−1<x0<x1/2<x3.