Rational Exponents means the exponent in p/q form. The exponent may be positive or negative.

3

4

5

In general, if n is any positive integer greater than one; x and y be rational numbers such that

and read as “nth root of y”. Here, n√ is called a radical, n is called the index of the radical and y is called the radicand.

The number written as y

1) √7 = 7

2) 7√250 = (250)

3) 4√(2/3) = (2/3)

1) 3

= √3

2) (101)

= 3√(101)

3) (3/4)

= 5√(3/4)

Let ‘a’ be any positive rational number and (m/n) be a positive rational number in the lowest form; then we write

1) (9)

= ( 9

= √729

= 27

2) (8)

= (8

=(64)

= 4

1) (125)

= ( 5 x 5 x 5)

= [ ( 5

= 5

= 5

= 5

= 5 x 5

= 25

2) (81)

= (3 x 3 x 3 x 3 )

= [(3

= 3

= 3

= 3

= 1

1) (4)

= 1/(4

= 1/(4

= 1/√64

= 1/8

2) (27)

= 1/(27)

= 1/(27

= 1/3√729

= 1/9

3) (49)

= 1/(49)

= 1/(49

= 1/√(49 x 49 x 49)

= 1/√(49 x 49 x 7 x 7)

= 1/(49 x 7)

= 1/343

• Laws of Exponents

• Rational Exponents

• Integral Exponents

• Scientific notation

• Solved examples on Scientific Notation

• Solved Examples on Exponents