Question

Write laws of indices on a chart. Express the product which contains two or more identical quantities in exponential notation by taking 5 different illustrations from our daily life situations

class-8​

Answer 1

Indices are a convenient tool in mathematics to compactly denote the process of taking a power or a root of a number. Taking a power is simply a case of repeated multiplication of a number with itself while taking a root is just equivalent to taking a fractional power of the number. Therefore, it is important to clearly understand the concept as well as the laws of indices to be able to apply them later in important applications.

We will first understand the formal notation for writing a number with an index, followed by the laws governing it

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Answer 2

A mathematical index is a number or variable raised to a power or exponent. Indices are the plural form of an index. Its laws are :

• xᵃ * xᵇ = xᵃ⁺ᵇ
• xᵃ ÷ xᵇ = xᵃ⁻ᵇ
• 1 ÷ xᵃ = x⁻ᵃ
• (xᵃ)ᵇ = xᵃᵇ
• x⁰ = 1
• (ab)ˣ = aˣ * bˣ
• xᵃ = xᵇ → a =b
• aˣ = bˣ → x = 0         {a ≠ b}

Daily Life Illustrations :

• Calculation of the area of the page of a square-shaped book → Suppose the side of the book is 15 cm, then its area would be 15² = 225 cm².
• Calculation of Compound Interest → CI = $P(1+\frac{R}{100})^T$, here P is Principal amount, R is Rate of interest, and T is Time period which is in index format.
• Calculation of Volume of Cubic tank → Suppose we need to find how much water can be stored in the tank, thus it can be given by the cube of the side of the tank = a³.
• Calculation of pH of water by purification systems → Drinking water should have a pH between 6.5 to 8.5 to be fit for drinking. It is given by [H⁺] = 10ˣ → pH = - log [H⁺] = - log 10ˣ = - x
• Calculation of Population increase → The population increase is an exponential growth calculated using indices and exponents framing a required formula.

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