Integral Exponents
In this section, we will discuss positive and negative integral exponents of rational numbers.
Positive Integral Exponents of a Rational Number
Let a/b any rational number and positive exponent to it be 'n' then
(a/b)
n = a/b x a/b x a/b x ....x n times
It means, (a x a x ...x n times)/(b x b x b x ...x n times )
In short it can written as,
(a/b)n = an/bn
Examples :
1) (3/2)
3
Solution :
(3/2)
3
= 3
3/2
3
= (3 x 3 x 3)/(2 x 2 x 2 )
= 27/8
2) (5/-3)
4
Solution :
(5/-3)
4
= 5
4/(-3)
4
= (5 x 5 x 5 x 5)/[(-3) x (-3) x (-3) x (-3)]
= 625/81
3) [(-2)/7]
3
Solution :
[(-2)/7]
3
= (-2)
3/7
3
=[(-2) x (-2) x (-2)]/(7 x 7 x 7)
= -8/343
4) (5/11)
0
Solution :
(5/11)
0
= 5
0/11
0
= 1/1
= 1
Negative Integral of a Rational Number
Let a/b any rational number and negative exponent to it be 'n' then
(a/b)
-n = 1 ÷ [a/b x a/b x a/b x ....x n times]
It means, 1 ÷ [(a x a x ...x n times)/(b x b x b x ...x n times )]
So, (a/b)
-n = (b x b x b x ...x n times)/(a x a x ...x n times)
[ As there is division so flip the numbers so a/b ----> b/a]
(a/b) -n = (b/a)n = bn/an
Examples :
1) (3/5)
-2
Solution :
(3/5)
-2
As the exponent is negative, so flip the numbers.
3/5 ----> 5/3 with positive exponent 2
(3/5)
-2 = (5/3)
2
(5/3)
2
= 5
2/3
2
= 25/9
2) [(-7)/2]
-3
Solution :
[(-7)/2]
-3
As the exponent is negative, so flip the numbers.
(-7)/2 ----> 2/(-7) with positive exponent 3
[2/(-7)]
3
= 2
3/(-7)
3
= 8/-343
Exponents
• Laws of Exponents
• Rational Exponents
• Integral Exponents
• Scientific notation
• Solved examples on Scientific Notation
• Solved Examples on Exponents
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