## NCERT Maths Solutions Class 8 Exponents and Power

*Class 8 Maths:* Chapter 12 Exponents and Power

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**Class 8 Maths.**

An Exponent stands for how many times the number is multiplied. We have studied in previous Class‘how to write large numbers using exponents’. It involves two numbers a and b where a is base and b is the exponent.

Mass of earth is 5,970,000,000,000,000,000,000,000 kg, which can be written as 5, 97 x 10 ^{ 24 }.

10^{ 24 } can be read as 10 raised to the power 24.

Now, we will find what is 2^{-2 } is equal to?

__Powers with negative exponents__

We know that 10 ^{ 2} = 10 x 10=100

As the exponents decrease by 1 the value becomes one-tenth of the previous value.

10 ^{ 1 }=100/10=10

10 ^{ 0 }=10/10=1

10 ^{ -1 }=1/10

10 ^{ 2 }=1/100

So, by observing the above pattern we can say that any integer ** a** which is non -zero, a

^{ -m }=1/ a

^{ m }, where

**is a positive integer.**

*m*a ^{ -m }Is the multiplicative inverse of a ^{ m } .

__Laws of exponents__

We know that for any non-zero integer ** a**,a

^{ m }x a

^{ n }=a

^{ m+n }

Example : -3

^{ -4 }x -3

^{ -3 }= 1/-3

^{ 4+3 }= -3

^{ -7}

-7 is the sum of exponents -4 and -3

Below mentioned laws also holds true, where a and b are non-zero integers and m, n are integers.

1. a ^{ m }/a ^{ n } = a ^{ m-n }

2. (a ^{ m }) x n = a ^{ m x n }

3. a ^{ m } x b ^{ n } = ab ^{ m }

4. a ^{ m }/a ^{ n } = a /b ^{ m }

5. a ^{0 } = 1

Note: -a ^{n } = 1 only if n=0. This will work for any an except a=1 or a=-1

**Use of exponents to express small numbers to standard forms**

Let’s observe a few cases as below:

• The distance from the earth to the sun is 149,600,000,000m.

• The thickness of the storybook is 20mm.

• Human hair thickness is 0.005 cm to 0.01 cm.

• The height of Mount Everest is 8848 m

• The average diameter of a red blood cell is 0.000007 mm

• The average radius of the Sun is 695000 km

• The thickness of a piece of paper is 0.0016 cm

Out of the above, few can be read very easily, there are some very large numbers and some very small numbers.

Let’s convert 0.000007 mm in the standard form

0.000007=7/10000000=7/10 ^{6 } = 7 x 10 ^{-6 } negative exponents.

NCERT Maths Solutions Class 8 very small numbers can be expressed in standard form using exponents.For any further questions related to this chapter, please visit online classes for ** Class 8**.

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