CBSE Notes For Class 8 Maths Chapter 10 Exponents and Powers

1.0Introduction 

Huge values like the distance between the Sun and Earth, or the mass of the Moon become too complicated to comprehend. Hence, in math, we use exponents, where the zeroes can simply be expressed as powers of ten.

For example, saying the mass of Earth is $5.7\times 10^{24}kg$ is much simpler than 5,970,000,000,000,000,000,000,000 kg.

2.0CBSE Class 8 Math Chapter 10 Exponents and Powers- Revision Notes

1. Powers with Negative Exponents

• When the exponent reduces by 1, the value decreases by one-tenth of the previous value. That is, $10^{-1}=\frac{1}{10}.$
• The same applies to any other base number used. Simply divide the previous number by the base.

2. Writing decimals in an expanded form

• To write the number 1234.56 in an expanded way with math, 

$1\times 1000+2\times 100+3\times 10+4\times 1+\frac{5}{10}+\frac{6}{100}$

$=1\times 10^3+2\times 10^2+3\times 10+4\times 1+5\times 10^{-1}+6\times 10^{-2}$

3. Laws of Exponents

• For any non-zero integer, $\text{ a, }{a}^m\times a^n=a^{m+n}.$
• In the same way, $\frac{a^m}{a^n}=a^{m-n}$

${\left(a^m\right)}^n=a^{mn}$

$a^m\times b^m=(ab{)}^m$

$a^m\times b^m=(ab{)}^m$

4. Exponents to Express Small Numbers in Standard Form

• Very small numbers, like the size of a rice grain or the thickness of paper, contain many decimal points, which can lead to confused math.
• For example, expressing the size of a plant cell as 0.00001275 meters is inconvenient but $1.27\times 10^{-5}$ is much clearer.
• Here, the key is to count how many jumps to the left

• in the decimal are needed to reach the first digit and then add it as a negative exponent. 
• If movements are made to the right, add to the exponent to get the standard form.

5. Comparing very large and very small numbers

• Standard form comes in handy when comparing very large numbers, like the diameters of celestial bodies.
• If one is to compare the diameter of the Sun, which is $1.4\times 10^9\mathrm{m}$ and the diameter of the Earth, which is $\text{ 1. }2756\times 10^7\mathrm{m}$
• Then you would get $\frac{1.4\times 10^9}{1.2756\times 10^7}=\frac{1.4\times 10^{9-7}}{1.2756}=\frac{1.4\times 100}{1.27}$, which is approximately equal to 100.
• This says that the diameter of the Sun is a hundred times that of the Earth.

3.0Solving Questions Related to Exponents and Powers

Question 1:  Evaluate: $\left(5^{-1}\times 2^{-1}\right)\times 6^{-1}$

We know that in math, $a^{-m}=\frac{1}{a^m}.$

So, the above expression can be written as $\left(\frac{1}{5}\times \frac{1}{2}\right)\times \frac{1}{6}$

Which becomes $\frac{1}{10}\times \frac{1}{6}=\frac{1}{60}.$

Question 2: Express 0.00000000323 in standard form

A number in a standard decimal form is $a\times 10^m$  where a is a non-zero digit and m can be either positive or negative.

With the given number, we shift the decimal point to the left 9 times to reach the standard form. Hence, the exponent would be negative.

The standard form of the given number is $3.23\times 10^{-9}.$

4.0Key Features of CBSE Maths Notes for Class 8 Chapter 10

• Maths notes are aligned with the latest CBSE math curriculum.
• Easy to understand, with simple examples.
• Crisp and short math explanations for quick revision.
• Notes are checked thoroughly and are 100% accurate.

5.0Sample Questions

Q1: What is a multiplicative inverse in math?

For any non-zero integer x, $x^{-z}=\frac{1}{x^z}$. Here. x is a positive integer and $x^{-z}$ is the multiplicative inverse of $x^z$.

Q2: When will $a^n$  be equal to one?

 Only when n=0,  $a^n$ is one.