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Click to Select a Page... Main Page Introduction Comparing The Math Operators I Comparing The Math Operators II Using Numbers 3 and Higher 1 ✱ b a ✱ 1 a ✱ 0 0 ✱ b a ✱ -b -a ✱ b -a ✱ -b Formula Summary So Far Integer a > 1 ✱ Decimal b > 1 Integer a > 1 ✱ Decimal 0 < b < 1 Integer a > 1 ✱ Decimal b < 0 Decimal a > 1 ✱ Decimal b > 1 Decimal a > 1 ✱ Decimal 0 < b < 1 Decimal a > 1 ✱ Decimal b < 0 Decimal 0 < a < 1 ✱ Decimal b > 1 Decimal 0 < a < 1 ✱ Decimal 0 < b < 1 Decimal 0 < a < 1 ✱ Decimal b < 0 Decimal -2 < a < 0 ✱ Decimal -1 < b < 2 Formula Summary So Far II Why 2 ✱ 0 is Not 1 Finding The Inverse Operations 1.25 ✱ -10 to 10 1.5 ✱ -10 to 10 1.75 ✱ -10 to 10 2 ✱ -10 to 10 2.5 ✱ -10 to 10 3 ✱ -10 to 10 3.5 ✱ -10 to 10 4 ✱ -10 to 10 4.5 ✱ -10 to 10 5 ✱ -10 to 10 6 ✱ -10 to 10 7 ✱ -10 to 10 8 ✱ -10 to 10 9 ✱ -10 to 10 10 ✱ -10 to 10 Fun With Math Strip Home Page DavesFunStuff Dave's Fun Stuff Find your favorite TV shows with "Let's Watch TV!" Dave's Fun Stuff SDN Media News and More Dave's Fun Stuff Super Birthdays Contact Webmaster

a ✱ 1

Now, let's look at the Superpowerition operation by placing the "1" to the right of the superpowerition notation symbol:

a ✱ 1

Let's try out some variables for a using the formula a ^ (a ^ (b - 1)) as it becomes a ^ (a ^ (1 - 1)).

2 ✱ 1 = 2 ^ (2 ^ (1 - 1)) = 2 ^ (2 ^ 0) = 2 ^ 1 = 2

3 ✱ 1 = 3 ^ (3 ^ (1 - 1)) = 3 ^ (3 ^ 0) = 3 ^ 1 = 3

6 ✱ 1 = 6 ^ (6 ^ (1 - 1)) = 6 ^ (6 ^ 0) = 6 ^ 1 = 6

10 ✱ 1 = 10 ^ (10 ^ (1 - 1)) = 10 ^ (10 ^ 0) = 10 ^ 1 = 10

1,000 ✱ 1 = 1,000 ^ (1,000 ^ (1 - 1)) = 1,000 ^ (1,000 ^ 0) = 1,000 ^ 1 = 1,000

As you can see, a ✱ 1 = a in every case above.

So, then, what does 1 ✱ 1 yield? Let's find out:

1 ✱ 1 = 1 ^ (1 ^ (1 - 1)) = 1 ^ (1 ^ 0) = 1 ^ 1 = 1

As predicted, the answer is "1".

In the exponent rules, n⁰ = 1 (where n > 0), 1ⁿ = 1, and n¹ = n.

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Fun With Math-Superpowerition: Inventing a Super Power Operation Main Page Introduction Comparing The Math Operators I Comparing The Math Operators II Using Numbers 3 and Higher 1 ✱ b a ✱ 1 a ✱ 0 0 ✱ b a ✱ -b -a ✱ b -a ✱ -b Formula Summary So Far Integer a > 1 ✱ Decimal b > 1 Integer a > 1 ✱ Decimal 0 < b < 1 Integer a > 1 ✱ Decimal b < 0 Decimal a > 1 ✱ Decimal b > 1 Decimal a > 1 ✱ Decimal 0 < b < 1 Decimal a > 1 ✱ Decimal b < 0 Decimal 0 < a < 1 ✱ Decimal b > 1 Decimal 0 < a < 1 ✱ Decimal 0 < b < 1 Decimal 0 < a < 1 ✱ Decimal b < 0 Decimal -2 < a < 0 ✱ Decimal -1 < b < 2 Formula Summary So Far II Why 2 ✱ 0 is Not 1 Finding The Inverse Operations 1.25 ✱ -10 to 10 1.5 ✱ -10 to 10 1.75 ✱ -10 to 10 2 ✱ -10 to 10 2.5 ✱ -10 to 10 3 ✱ -10 to 10 3.5 ✱ -10 to 10 4 ✱ -10 to 10 4.5 ✱ -10 to 10 5 ✱ -10 to 10 6 ✱ -10 to 10 7 ✱ -10 to 10 8 ✱ -10 to 10 9 ✱ -10 to 10 10 ✱ -10 to 10
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