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In this section, we will discuss positive and negative integral exponents of rational numbers.Let a/b any rational number and positive exponent to it be 'n' then

(a/b)

It means, (a x a x ...x n times)/(b x b x b x ...x n times )

In short it can written as,

1) (3/2)

(3/2)

= 3

= (3 x 3 x 3)/(2 x 2 x 2 )

= 27/8

2) (5/-3)

(5/-3)

= 5

= (5 x 5 x 5 x 5)/[(-3) x (-3) x (-3) x (-3)]

= 625/81

3) [(-2)/7]

[(-2)/7]

= (-2)

=[(-2) x (-2) x (-2)]/(7 x 7 x 7)

= -8/343

4) (5/11)

(5/11)

= 5

= 1/1

= 1

Let a/b any rational number and negative exponent to it be 'n' then

(a/b)

It means, 1 ÷ [(a x a x ...x n times)/(b x b x b x ...x n times )]

So, (a/b)

[ As there is division so flip the numbers so a/b ----> b/a]

1) (3/5)

(3/5)

As the exponent is negative, so flip the numbers.

3/5 ----> 5/3 with positive exponent 2

(3/5)

(5/3)

= 5

= 25/9

2) [(-7)/2]

[(-7)/2]

As the exponent is negative, so flip the numbers.

(-7)/2 ----> 2/(-7) with positive exponent 3

[2/(-7)]

= 2

= 8/-343

• Laws of Exponents

• Rational Exponents

• Integral Exponents

• Scientific notation

• Solved examples on Scientific Notation

• Solved Examples on Exponents

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