Using the Product Rule of Exponents, what is the exponent of 72⋅73 in exponential simplest form?
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add the exponents. In this case, we have 72 and 73, which have the same base. So, the exponent of 72⋅73 in exponential simplest form is 2 + 3 = 5.
To simplify the exponent of 72⋅73 using the Product Rule of Exponents, we need to add the exponents.
The Product Rule of Exponents states that when multiplying two numbers raised to the same base, you can add the exponents.
So, the exponent of 72⋅73 is calculated as follows:
72⋅73 = 7^2 ⋅ 7^3
According to the Product Rule, we add the exponents:
7^2 ⋅ 7^3 = 7^(2+3)
Simplifying the exponent 2+3, we get:
7^(2+3) = 7^5
Therefore, the exponent of 72⋅73 in exponential simplest form is 5.
To use the Product Rule of Exponents, we need to understand that when we're multiplying numbers with the same base, we can simply add their exponents.
In this case, we have 72⋅73. Both of these numbers have the base of 7, so we will add their exponents.
The first number, 72, can be written as 7² because 7² = 7⋅7 = 49.
The second number, 73, can be written as 7³ because 7³ =7⋅7⋅7 = 343.
Now we can multiply the two numbers together: 7² ⋅ 7³ = 49 ⋅ 343.
To simplify this expression, we can simply add the exponents together: 2 + 3 = 5.
Therefore, the exponent of 72⋅73 in exponential simplest form is 5.