Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Simplify 52 × 53. (write as a power, like 5^5)
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2 + 3 = 5, so 55 (= 3125).
2 Simplify a6 ÷ a2. (as a simplified expression)
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6 − 2 = 4, so a4.
3 What is 120?
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1.
Level 2 · Core
4 Simplify (x4)3. (as a simplified expression)
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4 × 3 = 12, so x12.
5 Simplify (3y2)3. (as a simplified expression)
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33 = 27 and y6, so 27y6.
6 What is 3−2? (as a fraction, like 1/9)
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1 ÷ 32 = 1/9.
Level 3 · Challenge
7 Simplify (2x3)2 × x4. (as a simplified expression)
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(2x3)2 = 4x6, then 4x6 × x4 = 4x10.
8 Simplify (3a2)2 ÷ a3. (as a simplified expression)
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9a4 ÷ a3 = 9a.
9 Can 23 × 34 be simplified using the index laws?
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No — the bases differ (2 and 3), and the laws require matching bases.