Exponents

Exponential notation or Power notation :
In a ^m , a is base m is called index or exponent or power

note : x^2 is x raised to power 2

Example : 5 ^4 = 5 * 5 * 5 * 5 ( 5 raised to power four)
a ^3 = a * a * a
x^ 7 = x * x * x * x * x * x * x
2 ^5 = 2 * 2 * 2 * 2 * 2
3^ 9 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3

practice:write expansion of
5 ^5 =
2^ 8 =
a ^6 =
x ^4 =

Example: find the value of 2^4
2 ^4 = 2 * 2 * 2 * 2 = 16

practice :find the value of
5^ 3
4^ 4
8^ 2
Answers:
125
256
64

Example :Express 81 as a power of 3 ( in power notation)
81 = 3 * 3 * 3 * 3 = 3 ^4 ( 3 raised to power 4)

practice : Express the following in power notation
64 as a power of 4
49 as a power of 7
625 as a power of 5
Answers:
4^3
7^2
5^4

Example : Simplify 3^4 + 5^3
(3 *3 * 3 * 3 ) + ( 5 * 5 * 5 )
81 + 125
206 is the answer

practice: simplify
5^6 + 7 ^3
9^3 + 6^4
2^6 + 3^5

Answers:
15968
2024
307

Example : simplify 2^5 - 5^2
(2 * 2 * 2 * 2 * 2 ) - ( 5 * 5 )
32 - 25 = 7 is the answer

practice : simplify
4^5 - 3^4
3^6 - 6^3
8^3 + 5^3

Answers:
943
513
6377^2 - 2^5