List two ways to write 3^7 as the product of two powers.
Way 1:
Way 2:
Way 1: 3^7 = (3^4) * (3^3)
Way 2: 3^7 = (3^6) * (3^1)
Explain why both of your expressions are equal to 3^7.
Both expressions are equal to 3^7 because of the exponent property that states, when multiplying powers with the same base, you add their exponents.
In Way 1, we have (3^4) * (3^3). The base (3) is the same in both terms, so we can combine them by adding the exponents: 3^(4 + 3) = 3^7.
In Way 2, we have (3^6) * (3^1). Again, since the base is the same (3), we can combine the terms by adding the exponents: 3^(6 + 1) = 3^7.
Therefore, both expressions are equivalent and equal to 3^7.
explain it like a 7th grader whos about to finish 7th grade
Sure! Imagine you have the number 3. We want to figure out how to write 3 multiplied by itself seven times. One way we can do this is by breaking it down into two parts.
In Way 1, we can write 3^7 as (3^4) * (3^3). This means we take 3 and multiply it by itself four times, and then multiply that answer by 3 again, but this time three times. When we add up all those multiplication results, we get the same answer as if we multiplied 3 by itself seven times.
In Way 2, we can write 3^7 as (3^6) * (3^1). This means we take 3 and multiply it by itself six times, and then multiply that answer by 3 just one more time. Again, when we add up those multiplication results, we get the same answer as if we multiplied 3 by itself seven times.
So, no matter if we break it down into (3^4) * (3^3) or (3^6) * (3^1), we get the same result as multiplying 3 by itself seven times, which is 3^7.