Question

the value of (3^0+4^-1)×2^2 is​

Answer 1

Answer:

(i) 3-2 = 1/32 = 1/9                                  [a-m = 1/ am]                       

(ii) (-4)-2 = 1/42 = 1/16                          [a-m = 1/ am]                   

(iii) (1/2)-5 = (2/1)5 = 25 = 32                [a-m = 1/ am]

Step-by-step explanation:

(i) (-4)5 ÷ (-4)8 = (-4)5-8                                  [am ÷ an = am-n]   

                         = (-4)-3

                         = 1/(-4)3                                [a-m = 1/ am]

                         = -1/64    

(ii) (1/23)2 = 12/(23)2                                    [(a/b)m = am/bm]

                   = 1/ 23*2                                     [(am)n = am*n]

                   = 1/26   

                   = 1/64

(iii) (-3)4 * (5/3)4 = (-3)4 * (54/34 )            [(a/b)m = am/bm]

                              = (3)4 * (54/34 )             [(-a)m = am when m is an even number]

                           = (3)4-4 * 54 

                           = 54

(iv)  (3-7 * 3-10) * 35 = 3-7-10+5                      [am * an = am+n]

                                  = 3-17+5

                                  = 3-12

                                  = 1/312                       [a-m = 1/ am]

(v) 2-3 * (-7)-3 = 1/23 * 1/(-7)-3                 [a-m = 1/ am]    

                        = 1/{(-7)3 * 23 }   

                        = 1/(-7 * 2)3                       [am * bm = (a * b)m]

                        = 1/(-14)3

                        = -1/(14)3                            [(-a)m = -am when m is an odd number]

Answer 2

Step-by-step explanation:

$( {3}^{0} + {4}^{ - 1}) \times {2}^{2} \\ \\ = (1 + \frac{1}{4}) \times 4 \\ \\ = \frac{5}{4} \times 4 \\ \\ = 5$