1. Simplifying exponents - Advanced

2. (30 + (32)-1) x 32 Rewriting 9 as the power of 3, 9 = 3 x 3 = 32
Example 1: Simplify ( ) x 32
Solution:
To simplify we need to convert all exponents having same base
We have 2 exponents with same base 3, hence we need to convert 9-1 with base as 3
( ) x 32
(30 + (32)-1) x 32 Rewriting 9 as the power of 3, 9 = 3 x 3 = 32
=( ) x 32 By applying the power rule, (am)n = am x n
By applying rule a-m=
After adding the unlike fraction
Ans: 10

3. Example 2: Simplify (70 + 49-1) ÷ 7-2 Solution:
To simplify we need to convert all exponents having same base
We have 2 exponents with same base 7, hence we need to convert 49-1 with base as 7
( ) ÷ 7-2
(70 + (72)-1) ÷ Rewriting 49 as the power of 7, 49 = 7 x 7 = 72
=( ) ÷ By applying the power rule, (am)n = am x n
By applying rule a-m=
After adding the unlike fraction
After applying division of fraction rule
=50 (Ans)

4. Converting negative power to positive
Example 3: Simplify
Solution:
Converting negative power to positive =
= (Ans)

5. = 25 - 2 – 22 = 32 – 2 – 4 = 32- 6 = 26 (Ans) Example 4: Simplify
Solution:
To simplify we need to convert exponents having same base. We have two exponents which can be converted with base as 2.
Rewriting 4 as the power of 2, 4 = 2 x 2 = 22
Rewriting 16 as the power of 2, 16= 2 x 2 x 2 x 2= 24
By applying the power rule, (am)n = amxn
(Making negative power as positive)
By applying the power rule, (am)n = amxn
Any number raised to the power 0 is 1
= – 22
= 32 – 2 – 4 = = 26 (Ans)

6. Try these