How to Evaluate Expressions with Powers

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?

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