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:

abac=a(b+c)

(ab)c=a(bc)

(ab)c=acbc

(ab)c=acbc

(ab)c=acbc=bcac

abac=a(bc)

ab=1ab

a0=1


Example

Let us study 40.5.
40.540.5=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:
40.540.5=22=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=24=2

For any real numbers a and b the following must be true:

a2=b,aisthesquarerootofb.

ifaj=bthenaisthejthrootofb.

jab=jajb

jab=jajb

b1j=jb

j must be a positive integer.


Video lesson

How can we rewrite 320,2?