EXPONENTS WITH PARENTHESES

Order of operations can be used to evaluate numerical expressions involving exponents with parentheses. 

1. Perform operations inside the parentheses.

2. Find the value of numbers with exponents.

3. Multiply or divide from left to right.

4. Add or subtract from left to right.

Example 1 :

Evaluate  the following :

6(36 ÷ 12)² + 8

Solution : 

=  6(36 ÷ 12)² + 8

Perform the operation inside the parentheses.

=  6(3)² + 8

Find the value of the number with exponent. 

=  6(9) + 8

Multiply. 

=  54 + 8

Add.

=  62

Example 2 :

Evaluate  the following :

12[(4 + 2)² ÷ 4] - 7

Solution : 

=  12[(4 + 2)² ÷ 4] - 7

Perform the operation inside the parentheses.

=  12[6² ÷ 4] - 7

Find the value of the number with exponent. 

=  12[36 ÷ 4] - 7

Perform the operation inside the brackets.

=  12[9] - 7

Multiply. 

=  108 - 7

Subtract.

=  101

Example 3 :

Evaluate  the following :

320 ÷ [(11 - 9)³ ÷ 2] ⋅ 8

Solution : 

=  320 ÷ [(11 - 9)³ ÷ 2] ⋅ 8

Perform the operation inside the parentheses.

=  320 ÷ [2³ ÷ 2] ⋅ 8

Find the value of the number with exponent. 

=  320 ÷ [8 ÷ 2] ⋅ 8

Perform the operation inside the brackets.

=  320 ÷ 4 ⋅ 8

Divide

=  80 ⋅ 8

Multiply.

=  640

Example 4 :

Evaluate  the following :

120 - [(4² - 1)² ÷ 25] ⋅ 2

Solution : 

=  120 - [(4² - 1)² ÷ 25] ⋅ 2

Find the value of the number with exponent inside the parentheses. 

=  120 - [(16 - 1)² ÷ 25] ⋅ 2

Perform the operation inside the parentheses.

=  120 - [15² ÷ 25] ⋅ 2

Find the value of the number with exponent. 

=  120 - [225 ÷ 25] ⋅ 2

Perform the operation inside the brackets.

=  120 - 9 ⋅ 2

Multiply.

=  120 - 18

Subtract.

=  102

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