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Division of Powers Practice
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Division of Powers Practice
Simplify each expression. Assume variables are non-zero where needed. Show working for questions that ask you to explain or evaluate.
The division law of indices
1.Complete the rule for dividing powers with the same base: bᵖ ÷ bᑫ = b^
2.Simplify 4⁹ ÷ 4⁵.
- 4⁴
- 4¹⁴
- 4⁴⁵
- 1⁴
3.Select every expression that can be simplified directly using the division law of indices.
- z¹¹ ÷ z⁶
- 9⁴ ÷ 3²
- 5⁸ ÷ 5³
- r⁷ ÷ s⁷
- n¹⁰ ÷ n⁴
Simplifying numerical powers
4.Simplify 6⁸ ÷ 6³.
5.Simplify 10⁹ ÷ 10⁴.
6.Simplify 3¹² ÷ 3⁷.
7.Simplify 8¹⁰ ÷ 8⁶.
Algebraic powers
8.Simplify x¹³ ÷ x⁸.
9.Simplify t¹⁶ ÷ t⁹.
10.Simplify c¹⁴ ÷ c⁶.
11.Simplify w²¹ ÷ w¹³.
Equal powers and order of operations
12.Simplify 9⁷ ÷ 9⁷.
13.Simplify p⁶ ÷ p⁶, assuming p ≠ 0.
14.Evaluate 3⁴ ÷ 3² + 2³. Follow the order of operations.
15.Evaluate (5⁵ ÷ 5³) × 4.
Explain, match and extend
16.Ari says 11⁹ ÷ 11⁴ = 1⁵. Explain the mistake and give the correct simplified answer.
17.Match each expression with its simplified form.
- 12⁸ ÷ 12³
- a¹⁰ ÷ a⁴
- 4⁹ ÷ 4⁹
- m¹⁵ ÷ m⁸
- q¹¹ ÷ q²
- 12⁵
- q⁹
- 1
- a⁶
- m⁷
18.Simplify (r¹² ÷ r⁵) ÷ r³ as a single power.
19.Write 2⁹ ÷ 2⁴ as a single power, then calculate its value.
4 printable pages
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