1. Law of Reciprocal

2. INTRODUCTION We know that a2 = a x a (1) (Here a is raised to the power 2, multiplying “a” 2 times) So, What is a-2? Here we notice the power is negative (- 2) Always, change negative powers to positive The following slides we are going to learn how to change
Negative power
Positive power

3. Changing negative powers to positive
Change power of a-2 to positive
Here we notice the power is negative (-2)
Rule to change negative powers to positive
Change power of a-2 in a denominator to positive
Here we notice the power in the denominator is negative (-2)
Rule to change negative powers in denominator to positive

4. By applying laws of reciprocals
Law of Reciprocals:
Rule 1: A number with negative exponent is converted into multiplicative inverse of the same number with positive exponent.
By applying laws of reciprocals
a-m
(we are reciprocating the number, so the negative power becomes positive)
a-m
It has negative power (-m)

5. By applying laws of reciprocals
Law of Reciprocals:
Rule 2: A number in a denominator with negative exponent is converted into multiplicative inverse of the same number with positive exponent.
By applying laws of reciprocals
(we are reciprocating the number, so the negative power becomes positive)
It has negative power (-m)

6. Avoid negative powers by making it positive
Examples
2-2 b-3
By Applying the rule,
Avoid negative powers by making it positive
By Applying the rule,
It has negative powers
(-2)
By Applying the rule,
Avoid negative powers by making it positive
By Applying the rule,
It has negative powers
(-3)
(-4)-5
By Applying the rule,
Avoid negative powers by making it positive
By Applying the rule,
It has negative powers
(-5)

7. Examples (-b)-3 By Applying the rule,
Avoid negative powers by making it positive
(-b)-3
By Applying the rule,
It has negative powers
(-3)
By Applying the rule,
Avoid negative powers by making it positive
By Applying the rule,
It has negative powers
(-4)
By Applying the rule,
Avoid negative powers by making it positive
By Applying the rule,
It has negative powers
(-5)

8. Fractional base with negative powers
Change power to positive
Here we notice the power is negative (-m)
Rule to change negative powers to positive

9. Changing rational number with negative powers to positive
To change rational number with negative power to positive power- reciprocate the rational number and make the power positive
Rule is

10. Examples for fractional base with negative powers
By Applying the rule,
Avoid negative powers by making it positive
By Applying the rule,
It has negative powers
(-2)
By Applying the rule, Avoid negative powers by making it positive
By Applying the rule,
It has negative powers
(-3)

11. Try these
Find the values of