Simplify expressions
We have to consider certain rules when we operate with exponents. Here follows the most common rules or formulas for operating with exponents or powers:
ab⋅ac=a(b+c)
(ab)c=a(b⋅c)
(ab)c=acbc
(ab)c=acbc
(ab)−c=a−cb−c=bcac
abac=a(b−c)
ab=1a−b
a0=1
Example
Let us study 40.5.
40.5⋅40.5=40.5+0.5=41=4
If we multiply 40.5 with itself the answer is 4. Since we know that if we multiply 2 with itself, the answer is also 4. Thus these numbers represent the same thing:
40.5⋅40.5=2⋅2=4
40.5=41÷2=√4=2
You may know that the more exact term for "the root of" is the "square root of". Sometimes you may choose to emphasize this by writing a two above the root sign:
√4=2√4=2
For any real numbers a and b the following must be true:
a2=b,aisthesquarerootofb.
ifaj=bthenaisthejthrootofb.
j√ab=j√a⋅j√b
j√ab=j√aj√b
b1j=j√b
j must be a positive integer.
Video lesson
How can we rewrite 320,2?