1. Simplification of Exponents

2. Example 1: Simplify 32 x 33
Solution:
32 x 33 . Here we have same base 3.
By applying the product rule, am x an = am+n
32 x 33 = 32+3 = 35 = 243
Example 2: 63 x 53
63 x 53 . Here we have same power 3.
By applying the same power rule, am x bm = (a x b)m
63 x 53 = (6 x 5)3
(6 x 5)3 = 303 = 27000

3. Example 3: Simplify 105 ÷ 102
Solution:
Here we have same base 10.
By applying the quotient rule, am ÷ an = am-n
105 ÷ 102 = = 103 = 1000
Example 4: Simplify
By applying Power of quotient rule,

4. Example 5: Simplify (43)2
Solution:
By applying power rule , (am)n = am x n
(43)2 = 43 x 2 = 46 = (46 = 4 X 4 X 4 X 4 X 4 X 4 = 4096)
Example 6: Simplify (34)0
Here we have to multiply the powers, (am)n = am x n
(34)0 = 34 x 0 = 30 = (any number raised to the power 0 is 1, a0 = 1)

5. Example 7: Solution = 1 (By applying number with zero exponent a0=1 )
Observe the product of first two exponents, they have same base and we can apply product rule
(By applying Quotient rule
= 1 (By applying number with zero exponent a0=1 )

6. Example 8: 10-4 Solution: Example 9: (6 x 5)3 Solution:
We know that by law of reciprocal a-m=
Example 9: (6 x 5)3
Solution:
There is no rule applied here. Find the product first and then find exponent.
(6 x 5)3 = 303 = 27000

7. Example 10:
Solution:
( By using power rule )

8. Example 11:
Solution:
( By using power rule

9. =3-6+4 x 2-6+8 x 42 (By applying the Product rule in
Cont……
(By using reciprocal rule)
=3-6 x 2-6 x 28 x 34 x 42
=3-6 x 34 x 2-6 x 28 x (Grouping the exponents based on their bases)
=3-6+4 x x 42 (By applying the Product rule in
=3-2 x 22 x 42 ( After applying integer rule)
(By using reciprocal rule )

10. Try these
Simplify:
23 x 25 b) 46÷43
c) d) (93)0
Solve: