list 2 different ways to write 3^7 as the product of 2 powers
1) (3^5) * (3^2) = 243 * 9 = 2187
2) (3^6) * (3^1) = 729 * 3 = 2187
does the * symbol mean multiplacation
Yes, the * symbol represents multiplication. So, when we write (3^5) * (3^2), it means we are multiplying 3 raised to the power of 5 with 3 raised to the power of 2.
explain why both of these expressions r equal to 3^7
Both expressions are equal to 3^7 because when we multiply exponential expressions with the same base, we add the exponents.
In the first expression, (3^5) * (3^2), we have 3 raised to the power of 5 multiplied by 3 raised to the power of 2. Since the base is the same (which is 3 in this case), we can simplify the expression by adding the exponents: 3^5 * 3^2 is equal to 3^(5 + 2) = 3^7.
In the second expression, (3^6) * (3^1), we have 3 raised to the power of 6 multiplied by 3 raised to the power of 1. Again, because the base is the same, we can simplify the expression by adding the exponents: 3^6 * 3^1 is equal to 3^(6 + 1) = 3^7.
Therefore, both expressions are equal to 3^7.