Exponent Problems | Negative Sign and Powers | Very important Concept | Class8 Ex 12.1 Q1 All Parts

Exponent Problems | Negative Sign and Powers | Very important Concept | Shortcut Tricks |

In this video, Concept of Negative sign and powers in Exponent problems are explained.
Problem discussed are:-
1) 3ˉ²
2) (-4)ˉ²
3) (1/2 )ˉ⁵

and similar Questions.
Whole concept is cleared by taking different examples.

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Class 8 Exponents and Powers Ex 12.1 Q1
Class 8 Exponents And Powers Negative Sign Problems
Q.1 Ex.12.1 Exponents and Powers
Negative Sign and power Mistakes
Negative sign
Power MIstakes


Exponents are powers or indices. An exponential expression consists of two parts, namely the base, denoted as b and the exponent, denoted as n. The general form of an exponential expression is b n. For example, 3 x 3 x 3 x 3 can be written in exponential form as 34 where 3 is the base and 4 is the exponent. They are widely used in algebraic problems, and for this reason, it is important to learn them so as to make the studying algebra easy.
Ex 12.1 Class 8 Maths Question 1.
Evaluate:
(i) 3-2
(ii) (-4)-2
(iii) (1/2)-5
Exponent Problems
Important Exponent Problems
How to Solve Exponent Problems
To help you understand the negative exponent rule better, this paper discusses in detail the following topics of negative exponent rule:

Negative exponents rule
Examples of negative exponents
Negative fractional exponents
How to solve Fractions with negative exponents
How to multiply negative exponents
Dividing negative exponents
Before we tackle each one of these topics, let us do a quick recap of the rules of exponents.

Multiplication of powers with same base: With multiplication of like bases, add the powers together.
Quotient of powers rule: When dividing like bases, the powers are subtracted
Power of powers rule: Multiply powers together when raising a power by another exponent
Power of a product rule: Distribute power to each base when raising several variables by a power
Power of a quotient rule: Distribute power to each base when raising several variables by a power
Zero power rule: This rule implies that, any base raised to a power of zero is equal to one
Negative exponent rule: To convert a negative exponent to a positive one, write the number into a reciprocal.
How to Solve Negative Exponents?
The law of negative exponents states that, when a number is raised to a negative exponent, we divide 1 by the base raised to a positive exponent. The general formula of this rule is: a -m = 1/a m and (a/b) -n = (b/a) n.

Example 1

Below are examples of how negative exponent rule works:

2 -3= 1/2 3 = 1/ (2 x 2 x 2) = 1/8 = 0.125
2 -2 = 1/2 2 = 1/4
(2/3) -2 = (3/2) 2
Negative fractional exponents
The base b raised to the negative power of n/m is equivalent to 1 divided by the base b raised to the positive exponent of n/m:

b -n/m = 1 / b n/m = 1 / (m √b) n

It implies that, if the base 2 is raised to the negative exponent of 1/2, it is equivalent to 1 divided by the base 2 raised to the positive exponent of 1/2:

2-1/2 = 1/21/2 = 1/√2 = 0.7071

You should notice that a fractional negative exponent is the same as finding the root of the base.

Fractions with negative exponents
The rule implies that, if a fraction a/b is raised to the negative exponent of n, it is equal to 1 divided by the base a/b raised to the positive exponent of n:

(a/b) -n = 1 / (a/b) n = 1 / (a n/b n) = b n/a n

The base 2/3 raised to the negative exponent of 2 is equal to 1 divided by the base 2/3 raised to the positive exponent of 2. In other words, 1 is divide by the reciprocal of the base raised to a positive exponent of 2

(2/3) -2 = 1 / (2/3) 2 = 1 / (2 2/3 2) = (3/2)2 = 9/4 = 2.25










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