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Law of Indices-Important Concepts & Problems

Law of Indices-Important Concepts & Problems

Definition

Concepts, Formulas And Problems on Indices

Let’s understand the definition with the help of an example:

can be expanded as 5×5×5.

i.e. we have multiplied 5 by itself 3 times. So, index (also known as exponent or power) tells us how many times we must multiply the number by itself.

Key Points:

  • 5 is called the base.
  • 3 is called the index (also known as power or exponent) because it indicates the power to which the base ‘5’ is raised.
  • 5³ is the index form (or power form) of 125.
  • The plural of index is known as indices.

Concepts, Formulas And Problems on Indices

Examples


Law of Indices

Rule 1: am × an = am + n

Concepts, Formulas And Problems on Indices

Law of Indices- Rule 1


Rule 2: am ÷ an = am ― n  if (a ≠ 0)

Concepts, Formulas And Problems on Indices

Law of Indices- Rule 2


Rule 3: a0 = 1  if (a ≠ 0)

Example: The value of (dx+y ÷ dx) ÷ d= ?

Solution: 

(dx+y ÷ dx) ÷ d= (dx+y-x) ÷ d ——————( applying the rule am ÷ an = am ― n)

= dy-y = d= 1


Rule 4: (ab)n = anbn

Example: The simplified value of 22 × 72 × y2 = ?

Solution:

22 × 72 × y2 = (2 × 7 × y)2 = (14y)2 = 196y2


Rule 5: (an)m = anm

Example: The value of [ { (2)}-2 ]-1 is equal to:

Solution: [ { (2)}-2 ]-1 = { (2)}-2×-1  = { (2)2 }2 = 22×2  = 2= 16


Concepts, Formulas And Problems on Indices

Law of Indices – Rule 6 & Rule 7


Rule 8: If am = an then m = n & if am = bm then a = b.

Example: Find the value of x, if 3x+1 + 3x = 36.

Solution:

3x+1 + 3x = 36.

3x × 3 + 3x = 36

3x × (3 + 1) = 36

3x = 9

3x = 32 ————–(applying the rule am = an then m = n)

∴ The value of x = 2

Those who are completely new to this topic, it’s my suggestion that you should practice at least 25-30 questions of varying degree of difficulty. So that you hold a good command on the application of various laws of indices.


Post Your Answer in Comment Section

  1. The value of (256)0.16 × (256)0.09 is _____________.
  2. If 5y+2 − 5y+1 = 500, then find the value of ‘y’.
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About the author

Knowledge Sharing

Knowledge Sharing is purely an educational blog which is maintained by Abhinav Prasad. Abhinav is currently pursuing MBA & he predominantly writes articles related to Aptitude and General Knowledge. He is also an enthusiastic learner and loves photography.

  • Struggler says:

    Thanks Abhinav. Nice explanation with beautiful style of presentation.

    • Abhinav Prasad says:

      Thank You Struggler. Try the last two questions and post your answer in the comments. All the best.

  • Struggler says:

    1) (256)^(0.16+0.09) = 2^(8*1/4)= 2^2 = 4
    2) y= 2


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