Chapter 2. Exponents and Radicals

MODULE - 1
Algebra
Exponents and Radicals
2. Express as a power of rational number with positive exponent:
Notes
4
3 −
⎛ ⎞
(i) ⎜ ⎟
⎝ 7 ⎠
⎡⎛
3
(ii) 5 −3
12 × 12 (iii) ⎢⎜
⎢⎣
⎝13
⎞
⎟
⎠
−3
⎤
⎥
⎥⎦
4
3. Express as a power of a rational number with negative index:
⎛ 3 ⎞
(i) ⎜ ⎟⎠
⎝ 7
4
2
[ ] 5
(ii) ( )
2
⎡⎛ 3 ⎞ ⎤
7 (iii) ⎢⎜
− ⎟ ⎥
⎢⎣
⎝ 4 ⎠ ⎥⎦
5
4. Simplify:
⎛ 3 ⎞
(i) ⎜ ⎟
⎝ 2 ⎠
−3
⎛ 3 ⎞
× ⎜ ⎟
⎝ 2 ⎠
7
(ii)
⎛
⎜ −
⎝
2 ⎞ ⎟
3 ⎠
−3
⎛ 2 ⎞ × ⎜ − ⎟
⎝ 3 ⎠
4
(iii)
⎛
⎜ −
⎝
7 ⎞ ⎟
5 ⎠
−4
⎛ ÷ ⎜ −
⎝
7 ⎞
⎟
5 ⎠
−7
5. Which of the following statements are true?
(i) a –m × a n = a –m–n
(ii) (a –m ) n = a –mn
(iii) a m × b m = (ab) m
(iv) a
m
÷ b
m
⎛
= ⎜
⎝
a
b
⎟
⎠
⎞
m
(v) a –m × a o = a m
2.6 MEANING OF a p/q
You have seen that for all integral values of m and n,
a m × a n = a m+n
What is the method of defining a 1/q , if a is positive rational number and q is a natural
number.
Consider the multiplication
a
=
1
q
× a
a q q
1
q
= a
1
q
1
q
× a ........ × a
q times
= a
1 1 1
+ + + .....q times
q q q
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Mathematics Secondary Course