I’m too dumb to get it
In: Mathematics
Exponents are a convenient way of showing repetitive multiplication of the same number. This is similar to multiplication showing repetitive addition of the same number.
so 3^(4) means I am going to multiply the base 3 by itself 4 (the exponent) times.
Whenever you multiply, 1 is a factor. A factor is an integer that can be multiplied by another integer to result in the original number.
So 10 = 2 x 5. but also 10 =1 x 2 x 5; 10=1 x 10
Now going back to exponents:
3^(4) = 3 x 3 x 3 x 3 By definition of exponential notation.
but we also need to remember that 3^(4) = 1 x 3 x 3 x 3 x 3. I like to call 1 the “invisible number of multiplication). It’s important to remember it is there.
so let’s look at a progression of exponents:
3^(4) = 1 x 3 x 3 x 3 x 3.
3^(3) = 1 x 3 x 3 x 3
3^(2) = 1 x 3 x 3
3^(1)= 1 x 3
3^(0) = 1
3^(0) indicates a multiplication operation where 3 is multiplied 0 times. But since it is multiplication, there must be some factor. Or yeah, 1 is always a factor in multiplication!
Also by the way:
3^(1)= 1 x 3 = 3 Any number to the first power = itself. Also the identity property of 1 says that any number times 1 =
itself.
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