Order of Operations with Exponents with practice worksheets PDF Download

Order of Operations with Exponents

 The rule to evaluate  the value of a mathematical expression that includes  exponents [e.g. ( 3^{2}  -6 ÷ 3)  x 8 ], is PEMDAS PEMDAS Stands for  P: Parentheses, E: Exponents ,  M:Multiplication , D: Division,  A: Addition and S: Subtraction.

order of operations with exponents

 

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) -8-3^{2}

Sol. (9+43-4) -8-3^{2}=  48-8-3^{2}         (Performing the operations inside the parentheses)

= 48-8-9             (solving exponent)

=31                       (performing subtraction)

(ii)  33+10-4^{2}÷2^{3}\times 31

Sol. 33+10-4^{2}÷2^{3}\times 31= 33+10-16÷8\times 31                            (performing exponents)

=33+10-2\times 31                                        (performing division)

=33+10-62                                             (performing multiplication)

= 43-62                                                     (performing addition)

= -19                                                           (performing subtraction)

(iii)  70÷7-3^{3}

Sol. 70÷7-3^{3}=  70÷7-27                      (performing exponent)

=10-27                               (performing division)

=-17                                     (solving subtraction)

(iv) \left ( 1^{4}\times 2^{2}+3^{3}\right )-2^{5}÷ 4

Sol. \left ( 1^{4}\times 2^{2}+3^{3}\right )-2^{5}÷ 4 = (1 x 4+27) -32 ÷ 4

=( 4+27) -32 ÷ 4

=31-32  ÷ 4

= 31- 8

= 23

(v)  25-8 x 2 +3^{2}

Sol. 25-8 x 2 +3^{2} =25-8 x 2 +9

= 25-16 +9

=9+9

=18

(vi) \mathbf{9^{2}+3\times \left ( 9-5 \right )^{2}}÷ 4

Sol.  9^{2}+3\times \left ( 9-5 \right )^{2}÷ 4 =9^{2}+3\times 4^{2}÷ 4

= 81  +3 x 16÷ 4

=81+48 ÷ 4

=81+12

=93

(vii) 36÷ \mathbf{[20-(4\times 2)]+4^{2}-6}

Sol.  36÷[20-(4\times 2)]+4^{2}-6= 36÷[20-8]+4^{2}-6                     (solving the operations inside the parentheses)

=36 ÷12+4^{2}-6

=36÷12+16-6                                 (solving exponent)

=3+16-6                                            (performing division)

=19-6                                                  (solving addition)

=13

(viii) \mathbf{\left ( 12+43-5 \right )-2+4^{2}}

Sol. \left ( 12+43-5 \right )-2+4^{2} =\left ( 55-5 \right )-2+4^{2}

=50-2+4^{2}

=50-2+16

= 48+16

= 64

(ix) (\mathbf{3\times 5^{2}} ÷ 15) \mathbf{-(5-2^{2})}

Sol. (3\times 5^{2}÷ 15) -(5-2^{2})=(3 x 25 ÷ 15) -(5-4)

=(75 ÷15)-(5-4)

= 5-4

=1

(x) \boldsymbol{2\times6 } ÷\boldsymbol{\left ( 8-2 \right )-2^{3}+3 \times 4} 

Sol.  2\times6 ÷\left ( 8-2 \right )-2^{3}+3 \times 4   =   2 x 6 ÷ 6 – 2^{3} +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)  ( 3^{2}  -6 ÷ 3)  x 8

(ii) \left ( 6+6^{2} \right )\times 3

(iii) 6^{2}-3\times \left ( 3^{2}\times 2 \right )+5

(iv) 5^{3}-54+8 \times 3

(v) 5+2^{3}\times(22÷ 11)-3^{2}\times (4+5)

(vi) 5+21÷ 3\times 2^{3}-61

(vii) 7+2^{2}\times 6+2^{2}-6

(viii) 2\times 5+3^{2}-96 ÷ 4

(ix) 12 ÷4\times 4^{2}\times 2^{2}

(x) 5^{2}\times 5-67

(xi) 33+10-4^{2}÷2^{3}\times 31

(xii) 6^{2}-24÷ 2^{3}  +14 x 3

(xiii) 9\times 9^{2}÷  3^{3}- 14

(xiv)  12+5\times 5^{3} ÷5-11

(xv) 2^{3}+45 ÷ 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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