Used formula (ab)n = anbn
1. (i) (-11)3 = (-1)3 x 113 = -121 x 11 = -1331
(ii) (-12)3 = -123 = -144 x 12 = -1728
(iii) (-21)3 = -213 = -441 x 21 = -9261
2. (i) -64 = -43 = (-4)3
(ii) -1056 = -25 x 33
i.e. -1056 is not a cube of negative integer.
(iii) -2197 = -133
(iv) -2744 = -143
(v) -42875 = -353
3. (i) -5832 = -23 x 36 = (-2 x 32)3 = (-18)3
(ii) -2744000 = -2744 x 103 = (-2 x 7 x 10)3 = (-140)3
4. (i) (7/9)3 \(=\frac{7^3}{9^3}\) = 343/729
(ii) (-8/11)3 \(=\frac{-8^3}{11^3}\) = -512/1331
(iii) (12/7)3 \(=\frac{12^3}{7^3}\) = 1728/343
(iv) (-13/8)3 \(=\frac{-13^3}{8^3}\) = -2197/512
(v) (2 2/5)3 = (12/5)3 \(=\frac{12^3}{5^3}\) = 1728/125 = 13 103/125
(vi) (3 1/4)3 = (13/4)3 \(=\frac{13^3}{4^3}\) = 2197/64 = 34 21/64
(vii) (0.3)3 = (3 x 10-1)3 = 33 x 10-3 = 27 x 10-3 = 0.027
(viii) (1.5)3 = (15 x 10-1)3 = 153 x 10-3 = 3375 x 10-3 = 3.375
(ix) (0.08)3 = (8 x 10-2)3 = 83 x 10-6 = 512 x 10-6 = 0.000512
(x) (2.1)3 = (21 x 10-1)3 = 213 x 10-3 = 9261 x 10-3 = 9.261
(5) (i) 27/64 \(=\frac{3^3}{4^3}\) = (3/4)3
(ii) 125/128 \(=\frac{125}{64\times2}=\frac{5^3}{4^3\times2}\) = 1/2 (5/4)3
Not a cube of rational number.
(iii) 0.001331 = 1331 x 10-6 = 113 x (10-2)3 = (11 x 10-2)3
= (0.11)3
(iv) 0.04 = 4/100 = 1/25 = (1/5)2
Not a cube of rational number.