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

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 2

write that In a form

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 \( 2^4 = 16 \).