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 = \(\frac{1}{a^{m}}\)

(iii) \(\frac{a^{m}}{a^{n}}\) = am – n = \(\frac{1}{a^{m - n}}\)

(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) (\(\frac{1}{4}\))-5

(vi) (\(\frac{1}{3}\))0


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

(ii) (-5)-4 = \(\frac{1}{(-5)^{4}}\); [Using the property of indices].

              = \(\frac{1}{(-5) × (-5) × (-5) × (-5)}\) ; [Using the definition of power].

              = \(\frac{1}{25 × 25}\)

              = \(\frac{1}{625}\) 

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

(iv) (\(\frac{1}{4}\))-5 = (4-1)-5 = 4(-1) × (-5) = 45 = 1024

Laws of Exponents
Properties of Exponents.

(vi) (\(\frac{1}{3}\))0 = 1; [Using the property of indices: here \(\frac{1}{3}\) ≠ 0].

9th Grade Math

From Laws of Indices to HOME PAGE

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.

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.

Share this page: What’s this?

Recent Articles

  1. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 24, 24 04:33 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  2. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  3. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More

  4. Numerator and Denominator of a Fraction | Numerator of the Fraction

    Feb 24, 24 04:09 PM

    What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.

    Read More

  5. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 24, 24 10:59 AM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More