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You've probably already seen that in math there are different ways of writing the same thing:
4 + 4 + 4 + 4 + 4
(repeated addition)
and
4 x 5 (multiplication)
Multiplication is a shorter and neater way of showing repeated addition.
In a similar way to how multiplication can be used in place of repeated addition, Powers can be used to show repeated multiplication.
3 x 3 x 3 x 3 x 3 (repeated multiplication)
and
3^{5} (Power)
Powers have two parts; a base and an exponent. There are different ways of "saying" powers that you might hear:

Memory Hint: base is on the bottom  like most bases!
The examples below will help with understanding how values, bases, exponents, powers, and repeated multiplication are related.
Power  Base  Exponent  Repeated Multiplication  Value 
4^{3}  4  3  4 x 4 x 4  64 
3^{5}  3  5  3 x 3 x 3 x 3 x 3  243 
2^{6}  2  6  2 x 2 x 2 x 2 x 2 x 2  64 
5^{4}  5  4  5 x 5 x 5 x 5  625 
7^{3}  7  3  7 x 7 x 7  343 
Power  Multiplication  
3^{5}
 3 x 3 x 3 x 3 x 3  
Multiply in steps  do two bases at
a time. Multiply the products by the remaining bases.  3 x 3 = 9  3 x 3 = 9  x 3 
9 x 9 = 81  x 3  
81 x 3 = 243  
Note: There are always different combinations of multiplication that produce the same answer. 
Try the worksheets below to practice working with exponents and bases.