Way 1: 3^7 = 3^6 * 3^1
Way 2: 3^7 = 3^5 * 3^2
List two different ways to write 3^7 to the product of two powers.
Way 1:
Way 2:
3 answers
Explain why both of your expressions are equal to 3^7
Both expressions are equal to 3^7 because they utilize the property of exponents which states that when multiplying two powers with the same base, we can simply add their exponents.
In Way 1, we break down 3^7 as (3^6) * (3^1). Since the base is the same (which is 3), we can add the exponents: 6 + 1 = 7. Therefore, (3^6) * (3^1) is equal to 3^7.
Similarly, in Way 2, we express 3^7 as (3^5) * (3^2). Again, using the exponent property, we add the exponents: 5 + 2 = 7. So, (3^5) * (3^2) is equivalent to 3^7.
Both expressions ultimately represent the same value of 3 raised to the power of 7.
In Way 1, we break down 3^7 as (3^6) * (3^1). Since the base is the same (which is 3), we can add the exponents: 6 + 1 = 7. Therefore, (3^6) * (3^1) is equal to 3^7.
Similarly, in Way 2, we express 3^7 as (3^5) * (3^2). Again, using the exponent property, we add the exponents: 5 + 2 = 7. So, (3^5) * (3^2) is equivalent to 3^7.
Both expressions ultimately represent the same value of 3 raised to the power of 7.
5 answers