T.W.
The pattern is easier to see as division rather than multiplication, perhaps.
Every time the exponent gets bigger, you're multiplying the number by itself once again. So,
3^4 = 3 x 3 x 3 x 3 = 81 (Sorry, can't find an alt code!)
3³ = 3 x 3 x 3 = 27
3² = 3 x 3 = 9
3¹ = 3
Conversely, then, each time you lower the exponent, you're *dividing* by the base number.
81 ÷ 3 = 27 (which is 3³)
27 ÷ 3 = 9 (which is 3²)
9 ÷ 3 = 3 (which is 3¹)
So going from
3¹ = 3
3º = 1 (which would be 3 ÷ 3)
And when you have negative exponents:
3^-1 = 1 ÷ 3 (or 1/3)
3^-2 = 1/3 ÷ 3 (or 1/9)
Hope this helps :-)
ETA: Ha! Ninja'd several times while I was looking for alt codes, lol! To me, they're easier to read, though :-)
@ Kristen - "because someone said so a long time ago" reminds me of 4th grade, when my teacher told us, "You can't divide by 0. You can't. It's impossible. Don't even try." And I wasn't one to question stuff like that, lol! Wasn't until I was volunteering in my kid's classroom, and *seeing* how division was done with math manipulatives, that I understood why!