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.
Level 1 · Warm-up
1 Evaluate 25.
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2 × 2 × 2 × 2 × 2 = 32.
2 Simplify a3 × a2.
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Add indices: 3 + 2 = 5 → a5.
3 Evaluate 90.
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Any non-zero base to the power 0 is 1.
Level 2 · Core
4 Simplify m7 ÷ m4.
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Subtract indices: 7 − 4 = 3 → m3.
5 Simplify (k4)3.
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Multiply indices: 4 × 3 = 12 → k12.
6 Simplify 4x3 × 3x5.
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Numbers multiply: 12; indices add: 8 → 12x8.
7 Evaluate 2−3.
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Negative index = reciprocal: 2−3 = 1/23 = 1/8. The minus never makes the answer negative.
Level 3 · Challenge
8 Simplify (3a2)3.
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33 = 27 and (a2)3 = a6 → 27a6. The cube hits the coefficient too.
9 Simplify 18y8 ÷ 6y8.
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18/6 = 3 and y8−8 = y0 = 1 → 3.
10 Simplify x2 ÷ x6, giving your answer with a positive index.
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x2−6 = x−4, and a negative index means reciprocal: 1/x4. (x−4 is equal but not a positive index!)
11 Write 5x−2 with a positive index.
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The index grabs only the x: 5/x2. The 5 stays on top.
12 Simplify (m2)4 × m3 ÷ m6.
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m8 × m3 = m11; then m11−6 = m5.