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 3c4d × 7c2d3.
Show worked solution
3 × 7 = 21, c4 × c2 = c6 and d1 × d3 = d4: 21c6d4. 10 adds the numbers; d3 forgets that d is d1; c8 multiplies the indices.
2 Simplify 2g5 × 4g3 ÷ g2. Write it as a number times a power of g.
Show worked solution
2g5 × 4g3 = 8g8, then 8g8 ÷ g2 = 8g6.
3 Find n if 43 × 4n = 411 ÷ 42.
Show worked solution
411 ÷ 42 = 49, and 43 × 4n = 43+n, so 3 + n = 9 and n = 6.
Level 2 · Core
4 Simplify (−2x2y4)3.
Show worked solution
(−2)3 = −8, (x2)3 = x6 and (y4)3 = y12: −8x6y12. −6 multiplies −2 by 3; +8 forgets that an odd power of a negative is negative; x5y7 adds the indices instead of multiplying.
5 Simplify 12h8 ÷ (2h)2.
Show worked solution
(2h)2 = 4h2, and 12h8 ÷ 4h2 = 3h6.
6 Work out 50 + (25 ÷ 22)2.
Show worked solution
50 = 1. Inside the bracket 25 ÷ 22 = 23, and (23)2 = 26 = 64. Total: 1 + 64 = 65.
Level 3 · Challenge
7 Three statements:
1 (a2b3)4 ÷ (ab)5 = a3b7
2 25 + 25 = 26
3 83 = 26
Which statements are correct?
1 (a2b3)4 ÷ (ab)5 = a3b7
2 25 + 25 = 26
3 83 = 26
Which statements are correct?
Show worked solution
(a2b3)4 = a8b12, and dividing by a5b5 leaves a3b7 (1 ✓). 25 + 25 is two lots of 25, which is 2 × 25 = 26 (2 ✓). 8 = 23, so 83 = (23)3 = 29, not 26 (3 ✗). 1 and 2.
8 (a mb)3 = 64m15, where a and b are whole numbers. Find a and b.
Show worked solution
Cubing the bracket gives a3 and m to the power 3b. So a3 = 64, giving a = 4, and 3b = 15, giving b = 5.
9 Find n if 45 × 8 ÷ 16 = 2n.
Show worked solution
45 = (22)5 = 210, 8 = 23 and 16 = 24. So 210 × 23 ÷ 24 = 29 and n = 9.