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

Simplify the expression x 4 y 2 3

Given that, x 4 y 2 3 Using law of indices x 4 3 = x 4 × 3 = x 12 And y 2 3 = y 6 Hence, x 4 y 2 3 = x 4 3 y 2 3 = x 12 y 6

Simplify the expression x 8 × x y 2 4 2 x 2 4

Given that, x 8 × x y 2 4 2 x 2 4 By using law of indices,first we simplify numerator, x 8 × x y 2 4 = x 8 × x 4 × y 2 4 = x 8 × x 4 × y 8 = x 12 y 8 ( x m × x n = x m + n ) And 2 x 2 4 = 2 4 × x 2 4 = 16 x 8 ( x m n = x m n Thus, x 8 × x y 2 4 2 x 2 4 = x 12 y 8 16 x 8 = 1 16 × x 12 x 8 × y 8 = 1 16 × x 12 - 8 × y 8 = 1 16 x 4 y 8 (Using x m ÷ x n = x m - n ) Hence, x 8 × x y 2 4 2 x 2 4 = 1 16 x 4 y 8

Simplify the expression 4 x 2 × 2 x 3 ÷ 2 x 0

Given that, 4 x 2 × 2 x 3 ÷ 2 x 0 By using law of indices, 4 x 2 × 2 x 3 = 4 × 2 × x 2 × x 3 = 8 x 5 ( x m × x n = x m + n ) And 2 x 0 = 1 a 0 = 1 4 x 2 × 2 x 3 ÷ 2 x 0 = 8 x 5 ÷ 1 = 8 x 5 Hence, 4 x 2 × 2 x 3 ÷ 2 x 0 = 8 x 5

Simplify the expression 4 x 2 y 3 2 2 x y 3

Given that, 4 x 2 y 3 2 2 x y 3 First we simplify the numerator 4 x 2 y 3 2 = 4 2 × x 2 2 × y 3 2 = 16 x 4 y 6 Denominator, 2 x y 3 = 2 3 × x 3 × y 3 = 8 x 3 y 3 Thus, 4 x 2 y 3 2 2 x y 3 = 16 x 4 y 6 8 x 3 y 3 = 16 8 × x 4 x 3 × y 6 y 3 = 2 × x 4 - 3 × y 6 - 3 = 2 x y 3 Hence, 4 x 2 y 3 2 2 x y 3 = 2 x y 3

E M B I B E

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Algebra>Chapter 2 - Making Sense of Algebra>Exercise 2.8

Karen Morrison and Nick Hamshaw Solutions for Exercise 8: Exercise 2.8

Author:Karen Morrison & Nick Hamshaw

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 8: Exercise 2.8

Attempt the practice questions from Exercise 8: Exercise 2.8 with hints and solutions to strengthen your understanding. Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition solutions are prepared by Experienced Embibe Experts.