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).

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