How to Evaluate Expressions with Powers

You may have heard that power corrupts, but rest assured that when mathematicians deal with powers, the order of operations usually keeps them in line. When an expression contains one or more powers, evaluate all powers from left to right before moving on to the Big Four operators. Here’s the breakdown:

1. Evaluate all powers from left to right.

   Raising a number to a power simply means multiplying the number by itself that many times. For example, 2³ = 2 x 2 x 2 = 8. Remember that anything raised to the 0 power equals 1.

2. Evaluate all multiplication and division from left to right.

3. Evaluate addition and subtraction from left to right.

Sample question

1. Evaluate 7 – 4² / 2⁴ + 9 s 2³.

   78. Evaluate all powers from left to right, starting with 4² = 4 x 4 = 16:

   = 7 – 16 / 2⁴ + 9 x 2³

   Move on to evaluate the remaining two powers:

   = 7 – 16 / 16 + 9 x 8

   Next, evaluate all multiplication and division from left to right:

   = 7 – 1 + 9 x 8

   = 7 – 1 + 72

   Finish up by evaluating the addition and subtraction from left to right:

   = 6 + 72

   = 78

Practice questions

1. Evaluate 3² – 2³ / 2².

2. Find 5² – 4² – (–7) x 2².

3. 70¹ – 3⁴ / –9 x –7 + 123⁰ = ?

4. What’s 11² – 2⁷ + 3⁵ / 3³?

Following are the answers to the practice questions:

1. 3² – 2³ / 2² = 7.

   First, evaluate all powers:

   3² – 2³ / 2² = 9 – 8 / 4

   Next, evaluate the division:

   = 9 – 2

   Finally, evaluate the subtraction:

   9 – 2 = 7

2. 5² – 4² – (–7) x 2² = 37.

   Evaluate all powers:

   5² – 4² – (–7) x 2² = 25 – 16 – (–7) x 4

   Evaluate the multiplication:

   = 25 – 16 – (–28)

   Finally, evaluate the subtraction from left to right:

   = 9 – (–28) = 37

3. 70¹ – 3⁴ / –9 x –7 + 123⁰ = 8.

   Evaluate all powers:

   70¹ – 3⁴ / –9 x –7 + 123⁰ = 70 – 81 / –9 x –7 + 1

   Next, evaluate the multiplication and division from left to right:

   = 70 – (–9) x –7 + 1 = 70 – 63 + 1

   Evaluate the addition and subtraction from left to right:

   = 7 + 1 = 8

4. 11² – 2⁷ + 3⁵ / 3³ = 2.

   First, evaluate all powers:

   11² – 2⁷ + 3⁵ / 3³ = 121 – 128 + 243 / 27

   Evaluate the division:

   = 121 – 128 + 9

   Finally, evaluate the addition and subtraction from left to right:

   = –7 + 9 = 2