Order of Operations with Powers and Roots
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Order of Operations with Powers and Roots
Order of operations with powers and roots for Grade 8: eight expressions with parentheses and brackets, powers, square roots, and fractions or decimals, then two problems that need a root or a power. With an answer key.
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- Skill
- Exponents Worksheets
- Pages
- 1
- Last updated
- Time
- About 20 minutes
- Answer key
- Included
- Goes with
- Order of Operations with Brackets
- Printing
- Black and white
- Related curriculum
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Use the rules for powers with the same base: add exponents to multiply, subtract them to divide, multiply them for a power of a power, and know that a zero exponent gives 1 and a negative exponent gives one over the power.
Reviewed by Mr. Robert Harrison, Teacher. How we check worksheets
How to use this sheet
- Have the child write a power out in full the first few times: 2 to the 3 is 2 × 2 × 2.
- For each rule, show it with expanded powers before using the rule: 2² × 2³ is five 2s multiplied.
- For negative exponents, use a pattern: 2³, 2², 2¹, 2⁰, then halve again for 2⁻¹.
Common mistakes
- Multiplying the base by the exponent, so 2³ becomes 6. It is 2 × 2 × 2, which is 8.
- Multiplying the exponents when multiplying powers with the same base. Add them: 2² × 2³ = 2⁵.
- Thinking a negative exponent makes a negative number, so 2⁻¹ is −2. It is 1/2.
- Thinking any number to the power 0 is 0. It is 1.
