How to Use Exponents in the Order of Operations

Problem

4 + 2^3 \times 3

Answer

28

The order of operations is parentheses, exponents, multiplication and division, then addition and subtraction. Exponents wait for nothing except parentheses.

Step-by-step solution

Apply the exponent first.
$2^3 = 2 \times 2 \times 2 = 8$
Why: Exponents come before multiplication and addition in the order of operations.
Rewrite the expression with the exponent evaluated.
$4 + 8 \times 3$
Why: Replacing the power keeps the rest of the expression unchanged.
Multiply.
$8 \times 3 = 24$
Why: Multiplication comes before addition.
Add.
$4 + 24 = 28$
Why: Addition is the last operation left.

Common mistakes

Doing 4 + 2 first and then raising 6 to a power.
Treating 2^3 as 2 times 3. The exponent counts factors, not multiplication by the base.
Multiplying 4 by 3 before the power is used.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$5 + 3^2 \times 2$

Show answer

$23$
$(4 + 2)^2 - 6$

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$30$
$36 \div (2 + 4) - 1$

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$5$
$3 \times (2^3 - 5)$

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$9$
$2^4 - 2 \times 5$

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$6$