Question

use the Product Rule of Exponents to simplify the expression 2 to the power of 4 use the Product Rule of Exponents to simplify the expression

Answer 1

write that In a form

Answer 2

The Product Rule of Exponents states that when you multiply two expressions with the same base, you add their exponents. The rule can be expressed as:

\[
a^m \times a^n = a^{m+n}
\]

However, the expression you provided, \(2^4\), is already in its simplest form, as it does not involve a product of terms that could be combined using the Product Rule.

If you meant to express \(2^4\) in a different way, we can break it down as follows:

\[
2^4 = 2 \times 2 \times 2 \times 2
\]

If you wanted to apply the Product Rule to a case such as \(2^2 \times 2^2\), you could use the rule to simplify it:

\[
2^2 \times 2^2 = 2^{2+2} = 2^4
\]

But overall, \(2^4\) is already a simplified expression. It evaluates to \(16\) if you perform the multiplication.

Answer 3

Sure! Here’s a more structured representation of the information:

### Expression Simplification Using the Product Rule of Exponents

**Given Expression:**
\[ 2^4 \]

**Using the Product Rule of Exponents:**
The Product Rule states that for any base \( a \) and exponents \( m \) and \( n \):
\[ a^m \times a^n = a^{m+n} \]

While the expression \( 2^4 \) itself cannot be simplified further, we can express it as a product of identical terms:

**Example Using the Product Rule:**
\[ 2^4 = 2^2 \times 2^2 \]

**Applying the Product Rule:**
\[
2^2 \times 2^2 = 2^{2 + 2} = 2^4
\]

**Value of \( 2^4 \):**
Calculating the value gives:
\[
2^4 = 16
\]

### Summary:
- The expression \( 2^4 \) is simplified as \( 2^2 \times 2^2 \).
- By applying the Product Rule, we confirm that \( 2^4 = 16 \).