Everything Maths Grade 10

Step 2: Simplify the exponents

=

22 n 22 n 21

24 n

=

22 n+2n+1

24 n

=

24 n+1

24 n

= 2^4 n+1(4n)

= 2

Worked example 3: Exponential expressions

QUESTION

Simplify:

52 x^1 
 9 x^2

152 x^3

SOLUTION

Step 1: Change the bases to prime numbers

52 x^1 : 9 x^2

152 x^3

=

52 x^1 :

(

32

)x 2

(53)^2 x^3

=

52 x^1 : 32 x^4

52 x^3 : 32 x^3

Step 2: Subtract the exponents (same base)

= 5(2x1)(2x3) 3 (2x4)(2x3)

= 5^2 x^1 ^2 x+3 32 x^4 ^2 x+3

= 5^2  3 ^1

Step 3: Write the answer as a fraction

=

52

3

=

25

3

Chapter 2. Exponents 47