Exponents: The Powers Worth Knowing

Exponents are the most powerful and most dangerous tool on the board. They can carry you to 37 in two dice, or overshoot into the hundreds. The difference is knowing which powers are worth reaching for.

The whole table

Dice show 1 to 6, so the complete set of powers available to you is small enough to memorise. These are the ones that land anywhere near useful:

The four that matter most

6^2 = 36 — one short of the target. The best exponent on the board.

2^5 = 32 — five short, and it only costs two small dice.

3^3 = 27 — ten short, useful when your board is full of threes.

5^2 = 25 — twelve short, and pairs naturally with a bracket.

Everything at or above 3^4 = 81 overshoots so badly that it is only useful if something else on the board can claw it back — which is rarer than it sounds, but see the last section.

The identity tricks

x to the power of 1

x^1 = x. Raising anything to the first power leaves it completely unchanged. This is the single most useful exponent in the game — not because of what it computes, but because it lets you satisfy the red power die without disturbing an equation that already works.

1 to the power of anything

1^x = 1, always. If you can build a term worth 1 — a lone 1 die, or a pair like 6/6 — it can sit under any exponent you like and stay 1.

A bracket as the power

The exponent does not have to be a single die. A bracket can supply it, which is how you reach a power your dice do not directly show.

1×4+2−5+6^(5−3) (5−3) = 2, so this is 6² = 36. Then 4+2−5 = +1. Two dice combine to make the power you needed.

Negative bases and even powers

A bracket that evaluates to a negative number can still be raised to a power, and the parity of that power decides the sign. An even exponent makes the result positive; an odd one keeps it negative.

(3−4)^4×5+6×5+2 (3−4) = −1, and (−1)⁴ = +1. So the first term is just 5. Then 30+2 finishes it.

This is a genuinely useful way to burn two awkward dice: any pair one apart gives you −1, and an even power turns it into a clean +1.

When overshooting is the plan

Occasionally the only path runs through a number far larger than 37. It works when a second large term cancels most of it.

(1×5+6)^3+2−6^4 11³ = 1331. Then 6⁴ = 1296 takes almost all of it back, leaving 35, and +2 finishes. Two enormous numbers, thirty-seven apart.

You will not need this often. But when a board looks impossible and has two big faces spare, checking whether their powers sit close together is worth ten seconds.

Division as the brake

The other way to survive a large power is to divide it back down. Powers of the same base are especially friendly here, because dividing one by another just subtracts the exponents.

2^5×6×3÷2^4+1 2⁵ = 32 multiplied up to 576, then divided by 2⁴ = 16 back down to 36. The two powers of 2 cancel to a factor of 2.

If you have two dice showing the same face, treat them as a matched pair of exponents rather than two separate problems. 2^5 ÷ 2^4 is just 2, and building that deliberately is often cleaner than trying to reach the same number by addition.

One caution: exponents bind tighter than multiplication, so 2*3^2 is 18 and not 36. If a solve is evaluating strangely, the order-of-operations guide is the place to look.