EXPONENTS 6

Simplify the following by writing in power form:

4w⁷⁰

  w¹⁰

Solution

= 4w^{70 - 10} 

= 4w⁶⁰

TRY THIS……………….

Simplify the following by writing in power form:

8 h⁵⁰

   h⁴⁰ 

INVERSE OF A MATRIX 1

ALGEBRA 1

Expand 8w(w – 5)

solution

= 8w(w – 5)

= (8w x w) – (8w x 5)

= 8w² – 40w answer

TRY THIS………..

Expand 13a(a+ 5)

FACTORIZATION 2

Factorize 49x² - 81y²

Solution

we use difference of two squares a² – b² = (a - b)(a + b)

49x²- 81y²  = 7²x² - 9²y²

                   = (7x)² - (3y)²

                   = (7x - 3y)( 7x + 3y)

Hence 49x² - 81y² = (7x - 3y)(7x + 3y)

TRY THIS………………………….

factorize 49x²- 121y²

FACTORIZATION 1

EXPONENTS 5

Write in expanded form: 4⁵

Solution

4⁵ = 4 x 4 x 4 x 4 x 4

TRY THIS……………….

Write in expanded form: 6⁴

COORDINATE GEOMETRY 1

Find the midpoint of a line from (13, 12) to (5, 10)

Solution

x1=13, x2=5, y1=12,y2=10.

Mid point = (x1 + x2, y1 + y2)

                          2             2

Mid point = (13 + 5,  12 + 10)

                         2          2

Mid point = (18, 22)

                      2     2

Hence midpoint = (9, 11)

TRY THIS……………………..

Find the midpoint of a line from (-4, 8) to (1, -2)

MATRIX 1

LOGARITHMS 2

If Log_ax = 44, find Log_a(¹/x).

Solution

= Log_a(¹/x)

= Log_ax^-1

= -1 x Log_ax    

= -1 x 44    (But Log_ax = 44)

= -44

TRY THIS………..

If Log_aw= 63, find Log_a(¹/w)

EXPONENTS 4

Simplify the following by writing in power form:

w⁷⁰

w¹⁰

Solution

= w^{70 - 10} 

=w⁶⁰

TRY THIS……………….

Simplify the following by writing in power form:

h⁵⁰

h²⁰