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YOUR STUDY SPACE · CBSE

Power Play — Class 8 Mathematics

Ganita Prakash Part 1 · Chapter 2

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Chapter summary

Power Play extends squares and cubes to general exponents and shows the astonishing pace of multiplicative (exponential) growth — for instance, a paper folded times would reach the Moon. The notation means multiplied by itself times; is the base and the exponent. The laws of exponents are developed from first principles: , , , , and . To keep the division law consistent, for , and negative exponents emerge as . Powers of ten let us write numbers in expanded form and, more powerfully, in scientific (standard) notation with , where the exponent matters more than the coefficient. The chapter uses this to compare gigantic real-world quantities — populations, distances, ages of the universe — and contrasts linear (additive) growth with exponential (multiplicative) growth.
Exponential notation and growthLaws of exponentsZero and negative exponentsPowers of tenScientific notation

Key ideas & terms

Base
The number being repeatedly multiplied in an exponential expression ; in the base is .
Exponent
The power telling how many times the base is multiplied by itself; in the exponent is .
Law of exponents
A rule such as or for combining powers of the same base.
Zero exponent
Any non-zero number to the power equals : for .
Negative exponent
A reciprocal power: , so .
Scientific notation
Writing a number as with , making very large or small numbers easy to read.

Extra questions & answers

Simplify .

Add exponents: .

What is equal to?

It equals ; raising a power to a power multiplies the exponents.

Why is for ?

Because , and any non-zero number divided by itself is .

Write as a fraction.

A negative exponent gives a reciprocal: .

Express in prime-factor exponential form.

.

Write in scientific notation.

, with coefficient between and .

Compute as a single power.

Using , it is .

What is ?

It is , because a negative number raised to an even power is positive.

Simplify as a power.

.

Why is the exponent more important than the coefficient in scientific notation?

Changing the exponent multiplies the value by a power of ten, while changing the leading digit only adjusts it slightly.