EXPONENTS A4

Simplify (e⁷)⁵

solution

= (e⁷)⁵

=  e^7x5

=  e³⁵

TRY THIS...........

Simplify  (f¹¹)⁴

ARITHMETICS A3

Evaluate 60 + 12 – 5 – 25 – 10 + 24.

Solution

= 60 + 12 – 5 – 25 – 10 + 24

= 60 + 12 + 24 – 5 – 25 – 10

= 60 + 12 + 24 – (5 + 25 + 10)

= 96 – 40

= 56

TRY THIS.......

Evaluate  70 + 34 – 27 – 38 – 25 + 46

LOGARITHMS B14

Evaluate Log₂(128 x 256).

Solution

= Log₂(128 x 256)

= Log₂128 +  Log₂256          (applying the product rule)

= Log₂2⁷ +  Log₂2⁸             ( 128= 2⁷ and 256=2⁸ )

= 7Log₂2 +  8Log₂2       ( remember  Log_aa^c = cLog_aa )

= (7 x 1) +  (8 x 1)          ( remember  Log_aa = 1 )

= 7 + 8

= 15

hence Log₂(128 x 256) = 15

TRY THIS..............

Evaluate Log₂(128 x 4).

EXPONENTS A3

Simplify (a⁴)⁵

solution

= (a⁴)⁵

=  a^4x5

=  a²⁰

TRY THIS.........

Simplify  (d¹⁰)⁶

ARITHMETICS A2

Evaluate 25 x 4618 + 5382 x 25

Solution

= 25 x 4618 + 5382 x 25

= 25 x (4618 + 5382)

= 25 x 10,000

= 250,000

Hence 25 x 4618 + 5382 x 25 = 250,000

TRY THIS…..

Evaluate 22 x 5851 + 4149 x 22

LOGARITHMS B13

Evaluate Log₂(1024 x 16).

Solution

= Log₂(1024 x 16)

= Log₂1024 +  Log₂16          (applying the product rule)

= Log₂2¹⁰ +  Log₂2⁴   ( 1024= 2¹⁰ and 16=2⁴ by prime factorization)

= 10Log₂2 +  4Log₂2       ( remember  Log_aa^c = cLog_aa )

= (10 x 1) +  (4 x 1)          ( remember  Log_aa = 1 )

= 10 + 4

= 14

hence Log₂(4 x 16) = 14

TRY THIS.......

Evaluate Log₂(1024 x 128).

EXPONENTS A2

Simplify (m⁴)²

solution

= (m⁴)²

=  m^4x2

=  m⁸

TRY THIS......

Simplify  (h¹⁰)²

ARITHMETICS A1

Evaluate  54 + 22 – 8 – 13 – 9 + 14

Solution

= 54 + 22 – 8 – 13 – 9 + 14

= 54 + 22 + 14 – 8 – 13 – 9

= 54 + 22 + 14 – (8 + 13 + 9)

= 90 – 30

= 60

TRY THIS.....

Evaluate  50 + 24 – 17 – 8 – 15 + 16

LOGARITHMS B12

Evaluate Log₂(8 x 32).

Solution

= Log₂(8 x 32)

= Log₂8 +  Log₂32          (applying the product rule)

= Log₂2³ +  Log₂2⁵             ( 8= 2³ and 32=2⁵ )

= 3Log₂2 +  5Log₂2       ( remember  Log_aa^c = cLog_aa )

= (3 x 1) +  (5 x 1)          ( remember  Log_aa = 1 )

= 3 + 5

= 8

hence Log₂(8 x 32) = 8 

TRY THIS.......

Evaluate Log₂(16 x 8).

EXPONENTS A1

Simplify (W¹¹)¹⁰

solution

= (W¹¹)¹⁰

=  W^11x10

=  W¹¹⁰

TRY THIS.....

Simplify  (X⁷)¹²