Simplify the expression 4 x × x × x 2

Given that, 4 x × x × x 2 First multiply the coefficients,and then we add the indices of variables 4 x × x × x 2 = 4 × 1 × x × x × x 2 4 × 1 × x × x × x 2 = 4 × x 1 + 1 + 2 = 4 x 4 Using law x m × x n = x m + n Hence, 4 x × x × x 2 = 4 x 4

Simplify the expression 4 x × x × x 2

Given that, 4 x × x × x 2 First multiply the coefficients,and then we add the indices of variables 4 x × x × x 2 = 4 × 1 × x × x × x 2 4 × 1 × x × x × x 2 = 4 × x 1 + 1 + 2 = 4 x 4 Using law x m × x n = x m + n Hence, 4 x × x × x 2 = 4 x 4

Simplify the expression x 2 2 ÷ 4 x 2

Given that, x 2 2 ÷ 4 x 2 First we open the bracket by using the law x m n = x m n x 2 2 = x 4 Thus, x 2 2 ÷ 4 x 2 = x 4 ÷ 4 x 2 = 1 4 × x 4 x 2 1 4 × x 4 x 2 = 1 4 × x 4 - 2 = 1 4 x 2 x m ÷ x n = x m - n Hence, x 2 2 ÷ 4 x 2 = x 2 4

Simplify the expression 11 x 3 × 4 a 2 b 2

Given that, 11 x 3 × 4 a 2 b 2 We can write it as, 4 a 2 b 2 = 4 2 × a 2 2 × b 2 = 16 a 4 b 2 11 x 3 × 16 a 4 b 2 = 11 × 16 × x 3 × a 4 b 2 = 176 x 3 a 4 b 2 Hence, 11 x 3 × 4 a 2 b 2 = 176 x 3 a 4 b 2

Simplify the expression x 8 ÷ x 3 2

Given that, x 8 ÷ x 3 2 By using x m n = x m n x 8 ÷ x 3 2 = x 8 ÷ x 6 By using, x m ÷ x n = x m - n x 8 ÷ x 6 = x 8 - 6 = x 2 x 8 ÷ x 3 2 = x 2

Simplify the expression 7 x 2 y 2 ÷ x 3 y 2

Given that, 7 x 2 y 2 ÷ x 3 y 2 We can write, x 3 y 2 = x 3 2 × y 2 = x 6 y 2 Now 7 x 2 y 2 ÷ x 3 y 2 = 7 x 2 y 2 x 6 y 2 7 x 2 y 2 x 6 y 2 = 7 × x 2 x 6 × y 2 y 2 = 7 × x 2 - 6 = 7 x - 4 = 7 x 4 Hence, 7 x 2 y 2 ÷ x 3 y 2 = 7 x 4

Simplify the expression 4 x 2 × 3 x 4 6 x 4

Given that, 4 x 2 × 3 x 4 6 x 4 By using law of indices,first we simplify numerator, 4 x 2 × 3 x 4 = 4 × 3 × x 2 × x 4 = 12 x 6 ( x m × x n = x m + n ) Thus, 4 x 2 × 3 x 4 6 x 4 = 12 x 6 6 x 4 12 x 6 6 x 4 = 12 6 × x 6 x 4 = 2 × x 6 - 4 = 2 x 2 (Using x m ÷ x n = x m - n ) Hence, 4 x 2 × 3 x 4 6 x 4 = 2 x 2