Nine laws of indics
Answers
heyy...!!
Law of Indices
To manipulate expressions, we can consider using the Law of Indices. These laws only apply to expressions with the same base, for example, 34 and 32 can be manipulated using the Law of Indices, but we cannot use the Law of Indices to manipulate the expressions 35 and 57 as their base differs (their bases are 3 and 5, respectively).
Six rules of the Law of Indices
Rule 1:
Any number, except 0, whose index is 0 is always equal to 1, regardless of the value of the base.
An Example:
Simplify 20:
Rule 2:
An Example:
Simplify 2-2:
Rule 3:
To multiply expressions with the same base, copy the base and add the indices.
An Example:
Simplify : (note: 5 = 51)
Rule 4:
To divide expressions with the same base, copy the base and subtract the indices.
An Example:
Simplify :
Rule 5:
To raise an expression to the nth index, copy the base and multiply the indices.
An Example:
Simplify (y2)6:
Rule 6:
An Example:
Simplify 1252/3:
The laws of indices
To manipulate expressions involving indices we use rules known as the laws of indices. The
laws should be used precisely as they are stated - do not be tempted to make up variations of
your own! The three most important laws are given here:
First law
a
m × a
n = a
m+n
When expressions with the same base are multiplied, the indices are added.
Example
We can write
7
6 × 7
4 = 76+4 = 710
You could verify this by evaluating both sides separately.
Example
z
4 × z
3 = z
4+3 = z
7
Second Law
a
m
a
n
= a
m−n
When expressions with the same base are divided, the indices are subtracted.
Example
We can write
8
5
8
3
= 85−3 = 82
and similarly z
7
z
4
= z
7−4 = z
3
Third law
(a
m)
n = a
mn
Note that m and n have been multiplied to yield the new index mn.
Example
(64
)
2 = 64×2 = 68
and (e
x
)
y = e
xy
It will also be useful to note the following important results:
a
0 = 1, a1 = a
Step-by-step explanation:
the 9 laws I hope it may be help u
