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**Order of Operations with Exponents**

** **The rule to evaluate the value of a mathematical expression that includes exponents [e.g. ( -6 ÷ 3) x 8 ], is **PEMDAS . ** PEMDAS Stands for P: Parentheses, E: Exponents , M:Multiplication , D: Division, A: Addition and S: Subtraction.

The following steps must be followed to solve a mathematical expression that includes an exponents:

Step 1: Operations inside the parentheses should be solved first .

Step 2: After performing operations inside of parenthesis , solve the exponents .

Step 3: After the parentheses and the exponents, perform multiplication or division from left to right depending on which operation comes first.

Step 4: Finally, after multiplication and division, perform addition and subtraction from left to right depending on which operation comes first.

**Order of Operations with Exponents(Solved examples) **

**(i)** (9+43-4) -8-

Sol. (9+43-4) -8-= 48-8- (Performing the operations inside the parentheses)

= 48-8-9 (solving exponent)

=31 (performing subtraction)

**(ii) **33+10-÷

Sol. 33+10-÷= 33+10-16÷ (performing exponents)

=33+10-2 (performing division)

=33+10-62 (performing multiplication)

= 43-62 (performing addition)

= -19 (performing subtraction)

**(iii) 70÷7-**

Sol. 70÷7-= 70÷7-27 (performing exponent)

=10-27 (performing division)

=-17 (solving subtraction)

**(iv) **÷ 4

Sol. ÷ 4 = (1 x 4+27) -32 ÷ 4

=( 4+27) -32 ÷ 4

=31-32 ÷ 4

= 31- 8

= 23

**(v)** 25-8 x 2 +

Sol. 25-8 x 2 + =25-8 x 2 +9

= 25-16 +9

=9+9

=18

**(vi) ÷ 4**

Sol. ÷ 4** =**÷ 4

= 81 +3 x 16÷ 4

=81+48 ÷ 4

=81+12

=93

**(vii) 36÷ **

Sol. 36÷**= **36÷[20-8] (solving the operations inside the parentheses)

=36 ÷12

=36÷12+16-6 (solving exponent)

=3+16-6 (performing division)

=19-6 (solving addition)

=13

**(viii)**

Sol. =

=

=50-2+16

= 48+16

= 64

**(ix) ( ÷ 15) **

Sol. **(÷ 15**) **=**(3 x 25 ÷ 15) -(5-4)

=(75 ÷15)-(5-4)

= 5-4

=1

**(x) ÷ **

Sol. ** ÷ ** = 2 x 6 ÷ 6 – +3 x 4

= 2 x 6 ÷ 6 – 8 +3 x 4

= 12 ÷ 6 – 8 +3 x 4

=2 – 8 +3 x 4

=2-8+12

=-6+12

=6

**Order of Operations with Exponents (Unsolved examples with answers)**

**(i)** ( -6 ÷ 3) x 8

**(ii)**

**(iii)**

**(iv)**

**(v)** (22÷ 11)

**(vi)** 5+21÷

**(vii)**

**(viii)** ÷ 4

**(ix)** 12 ÷4

**(x)**

**(xi)** 33+10-÷

**(xii) ÷ **+14 x 3

**(xiii) **÷

**(xiv) ** ÷5-11

**(xv)** ÷ 9

**Ans.** (i) 56 (ii) 126 (iii) -13 (iv) 95 (v) -60 (vi ) 0 (vii) 29 (viii) -5 (ix) 67 (x) 58 (xi) -19 (xii) 75 (xiii) 13

(xiv) 126 (xv) 13

**Order of Operations with Exponents worksheet PDF with answers**

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