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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

What do you do first in order of operations ?

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

(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

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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Order of Operations with Exponents

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