Everything Maths Grade 10

SOLUTION

Step 1: Change the bases to prime numbers

9 x 1

3 x+ 1

=

(

32

)x

 1

3 x+ 1

=

32 x 1

3 x+ 1

Recognise that 32 x= (3x)^2

Step 2: Factorise using the difference of squares

=

(3x1) (3x+ 1)

3 x+ 1

Step 3: Cancel the common factor and simplify

= 3x 1

Exercise 2 – 1:

Simplify without using a calculator:

1. 160 2. 16 a^0 3. 119 x 112 x


2. 106 x 102 x 5. ( 6 c)^3 6. ( 5 n)^3

7.

2 ^2

32

8.

5

2 ^3

9.

(

2

3

) 3

10.

a^2

a^1

11.

xy^3

x^4 y

12. x^2 x^3 t+1


13. 3  32 a 32 14.
    2 m+20
    2 m+20

15.

2 x+4

2 x+3

16. (2a^4 )(3ab^2 ) 17.(7m^4 n)(8m^6 n^8 ) 18.2(a^7 b^8 )( 4 a^3 b^6 )( 9 a^6 b^2 )


17. ( 9 x^3 y^6 )

(

1

9

x^8 y^7

) (

1

5

x^3 y^6

)

20.

a^3 x

ax

21.

20 x^10 a^4

4 x^9 a^3

22. 18 c^10 p^8
    9 c^6 p^5

23.

6 m^8 a^10

2 m^3 a^5

24. 312  39

25.

7(a^3 )^3

a^7

26.

9(ab^4 )^8

a^3 b^5

27.

22

62

28.

(

a^6

b^7

) 5

29.

(

2 t^4

) 3

30.

(

3 n+3

) 2

31.

3 n 9 n^3

27 n^1

32.

13 c+ 13 c+2

3  13 c 13 c

33.

35 x 815 x 33

98 x

Chapter 2. Exponents 49