Why is the answer of, "a number to the power of zero" 1 and not 0? ? show your work.

It helps to go back to how exponents first come up: as an abbreviation for lots of multiplications. We abbreviate a whole bunch of things in math - multiplication first comes up as an abbreviation for repeated addition; we could write out 3 + 3 + 3 + 3 + 3 + 3 every time we want to say "3, six times", but it's much more convenient to write it as "3 x 6" and save yourself the paper space and pencil lead.

Exponentiation comes as the next step up; when we've got something like 3 x 3 x 3 x 3 x 3 x 3 - 6 3's being multiplied together - we can abbreviate it with the exponent instead of writing out all of those individual 3's and multiplication signs. Here are the first few "powers" of 3 and their abbreviations:

Notice that each time the exponent goes up, our number gets multiplied by 3. What if we went in the other direction? We'd be doing the exact opposite thing as the exponents went down - we'd be dividing by 3 each time.

And we can continue this pattern one more time to find that

There's nothing special about our choice of number, by the way. We could say the same about 5:

or 7:

Or any number we want - any number raised to the 0 power will always give us 1, because any number divided by itself is 1.

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get