Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 30
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37MODULE -
1
Exponents and Radicals
Algebra
+
−
2
3
2
3
+
3. Simplify:
−
+
2
3
2
3
Notes
1
4. Rationalise the denominator of
−
−
3
2
1
1
+ .
a
=
3 +
5. If
. Find
a
2
2
a
+
2
5
7
=
+
x
7
y
6. If
, find x and y.
−
2
5
7
______________________________________________________________
LET US SUM UP
•
m
a × a × a × ..... m times = a
is the exponential form, where a is the base and m is the
exponent.
•
Laws of exponent are:
m
⎛
⎞
m
a
a
=
⎜
⎟
÷ a
m
n
m+n
m
n
m–n
m
m
m
(i) a
× a
= a
(ii) a
= a
(iii) (ab)
= a
b
(iv)
⎝
⎠
m
b
b
1
( )
−
=
m
n
=
a
o
(v)
m
mn
(vi) a
= 1
(vii)
a
a
m
a
p
•
a =
q
q
p
a
•
An irrational number
x is called a surd, if x is a rational number and nth root of x is
n
not a rational number.
•
In
x , n is called index and x is called radicand.
n
•
A surd with rational co-efficient (other than 1) is called a mixed surd.
•
The order of the surd is the number that indicates the root.
•
The order of
x is n
n
•
Laws of radicals (a > 0, b > 0)
n
[ ]
a
a
=
n
=
×
=
n
(i)
(ii)
(iii)
n
n
n
n
a
b
ab
a
a
n
b
b
68
Mathematics Secondary Course
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