Laws of Indices

We will discuss here about the different Laws of Indices.

If a, b are real numbers (>0, ≠ 1) and m, n are real numbers, following properties hold true.

(i) am × an = am + n

(ii) a-m = 1am

(iii) aman = am – n = 1amn

(iv) (am)n = amn

(v) (ab)n = an ∙ bn

(vi) a0 = 1

(vii) if am = an then m = n.

(viii) if an = bn, a ≠ b then n = 0.


Note: Some of the above properties hold true for any two real numbers a, b. Laws (i) to (v) hold true for any two real numbers a, b. Also note that 10 = 1.


Laws of Indices or Exponents

Problems on knowledge and use of the properties of indices:

1. Determine the numerical value for each of the following (not containing exponents):

(i) 64

(ii) (-5)-4

(iii) 90

(iv) (14)-5






(vi) (13)0


Solution:

(i) 64 = 6 × 6 × 6 × 6 = 1296; [Using the definition of power/exponent].

(ii) (-5)-4 = 1(5)4; [Using the property of indices].

              = 1(5)×(5)×(5)×(5) ; [Using the definition of power].

              = 125×25

              = 1625 

(iii) 90 = 1; [Using the property of indices: here 9 ≠ 0].

(iv) (14)-5 = (4-1)-5 = 4(-1) × (-5) = 45 = 1024

Laws of Exponents
Properties of Exponents.

(vi) (13)0 = 1; [Using the property of indices: here 13 ≠ 0].







9th Grade Math

From Laws of Indices to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Divisible by 2 | Test of Divisibility by 2 |Rules of Divisibility by 2

    Mar 17, 25 04:04 PM

    Divisible by 2
    A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

    Read More

  2. Worksheet on 7 Times Table | Printable Multiplication Table | Video

    Mar 17, 25 02:41 PM

    worksheet on multiplication of 7 times table
    Printable worksheet on 7 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More

  3. Worksheet on 6 Times Table | Printable Multiplication Table | Video

    Mar 16, 25 03:09 PM

    worksheet on multiplication of 6 times table
    Printable worksheet on 6 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More

  4. Worksheet on 5 Times Table | Printable Multiplication Table | Video

    Mar 16, 25 01:25 PM

    worksheet on multiplication of 5 times table
    Printable worksheet on 5 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More

  5. Worksheet on 3 Times Table | Printable Multiplication Table | Video

    Mar 16, 25 12:59 PM

    worksheet on multiplication of 3 times table
    Printable worksheet on 3 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More