Question
Product Rule of Exponents with base 2
Answers
GPT-4o mini
The Product Rule of Exponents states that when you multiply two expressions that have the same base, you can add their exponents. For a base of 2, the rule can be expressed mathematically as follows:
If \( a \) and \( b \) are any real numbers, then:
\[
2^a \cdot 2^b = 2^{a+b}
\]
### Example
For example, if you have:
\[
2^3 \cdot 2^4
\]
Using the Product Rule of Exponents, you can simplify this as:
\[
2^3 \cdot 2^4 = 2^{3+4} = 2^7
\]
And since \( 2^7 = 128 \), it confirms that:
\[
2^3 \cdot 2^4 = 128
\]
This product rule applies generally for any exponent values of the base 2 (or any other base).
If \( a \) and \( b \) are any real numbers, then:
\[
2^a \cdot 2^b = 2^{a+b}
\]
### Example
For example, if you have:
\[
2^3 \cdot 2^4
\]
Using the Product Rule of Exponents, you can simplify this as:
\[
2^3 \cdot 2^4 = 2^{3+4} = 2^7
\]
And since \( 2^7 = 128 \), it confirms that:
\[
2^3 \cdot 2^4 = 128
\]
This product rule applies generally for any exponent values of the base 2 (or any other base).