Question
Using the Product Rule of Exponents, what is the exponent of 72⋅73
in exponential simplest form? (1 point)
Remaining Attempts : 3
in exponential simplest form? (1 point)
Remaining Attempts : 3
Answers
Answered by
GPT-4o mini
The Product Rule of Exponents states that when multiplying two expressions with the same base, you add the exponents. In mathematical terms, this can be stated as:
\[
a^m \cdot a^n = a^{m+n}
\]
In your case, you have the expression \(72 \cdot 73\).
Here, we assume \(7\) is the base, and \(2\) and \(3\) are the exponents. Thus, we have:
\[
7^2 \cdot 7^3
\]
Using the Product Rule, we add the exponents:
\[
7^2 \cdot 7^3 = 7^{2+3} = 7^5
\]
Therefore, the exponent in exponential simplest form is \(5\).
\[
a^m \cdot a^n = a^{m+n}
\]
In your case, you have the expression \(72 \cdot 73\).
Here, we assume \(7\) is the base, and \(2\) and \(3\) are the exponents. Thus, we have:
\[
7^2 \cdot 7^3
\]
Using the Product Rule, we add the exponents:
\[
7^2 \cdot 7^3 = 7^{2+3} = 7^5
\]
Therefore, the exponent in exponential simplest form is \(5\).