The Power law of exponents states that,
For any non-zero integer a, (𝑎𝑚)𝑛 = 𝑎𝑚𝑛,where m and n are integers.
For example,
(32)4 = 32×4 = 38.
Importance of parenthesis
An important point of the power law is the use of the parenthesis.
Consider two numbers, (22)3 and 23
In the first number, we can use the power law and write it as (22)3 = 26.
In the second number, the base is 2 and the exponent is 23 = 8. So we write the number as
28.
Due to the use of brackets, the first number is read as ‘2 raised to 2, the whole raised to 3’. While the second number is read as ‘2 raised to 2 raised to 3’.
Summary
| Power Law of Exponents | For any non-zero integer ‘a’, where ‘m’ and ‘n’ are whole numbers,
(𝑎𝑚)𝑛 = 𝑎𝑚𝑛 |