There are 8 Laws of Exponents.

1) If the bases are same and there is a multiplication between them then, add the exponents keeping the base common.

a^{m} x a^{n } = a ^{( m + n )} |

i) 3

= 3

ii) b

= b

= b

= b

(iii) (-6)

= (-6)

= (-6)

(iv) 8

= 8

= 8

If the bases are same and there is a division between them then, subtract the 2nd exponent from the 1st keeping the base common.

a^{m}÷ a^{n } = a ^{( m - n )} |

(i) 4

= (4 x 4 x 4 x 4 x 4)/(4 x 4 x 4)

= 4

= 4

(ii) p

= p

(iii) 8

= 8

= 8

(iv) 15

= 15

= 15

(v)(5/2)

= (5/2)

= (5/2)

3) If there are double exponents then, multiply the exponents and keep the base same.

( a^{m}) ^{n} = a^{(m x n )} = a^{mn} |

(i) (2

= 2

= 2

(ii)(-8

= (-8)

= (-8)

(iii) (y

= y

= y

4) Any number with exponent zero ,the answer is 1.

a ^{0} = 1 |

(i) (1000)

= 1

(ii) a

= 1

(iii) (-25)

= 1

5) If the exponent is 1 then the number itself is the answer.

a^{1} = a |

(i) 20

= 20

(ii) b

= b

(iii) (2000)

= 2000

6) If the exponent is negative so to make it positive write the reciprocal of it.

a^{-m} = 1/a^{m} |

1/a^{-m} = a^{m} |

i) 4

= 1 / 4

= 1 / 16

2) 1 / 3

= 3

7) Two different bases have same exponents then bring the two bases under common parenthesis and keep the same exponent.

a^{m} x b^{m} = (ab)^{m} |
a^{m} ÷ b^{m} = (a/ b)^{m} |

(i) 2

= ( 2 x 3 )

= 6

= 6 x 6 = 36

(ii) 6

= ( 6/3)

= 2

= 2 x 2 = 4

(iii) 3

= 3

= 3

= 81 / 27

= 3

• Laws of Exponents

• Rational Exponents

• Integral Exponents

• Scientific notation

• Solved examples on Scientific Notation

• Solved Examples on Exponents