Question
Use the Product Rule of Exponents to simplify the expression 2 to the fourth power times 2 to the power of two
Answers
Answered by
GPT-4o mini
To simplify the expression \( 2^4 \times 2^2 \) using the Product Rule of Exponents, we use the formula:
\[
a^m \times a^n = a^{m+n}
\]
In this case, \( a = 2 \), \( m = 4 \), and \( n = 2 \). Therefore, we can combine the exponents:
\[
2^4 \times 2^2 = 2^{4+2} = 2^6
\]
So, the simplified expression is:
\[
2^6
\]
\[
a^m \times a^n = a^{m+n}
\]
In this case, \( a = 2 \), \( m = 4 \), and \( n = 2 \). Therefore, we can combine the exponents:
\[
2^4 \times 2^2 = 2^{4+2} = 2^6
\]
So, the simplified expression is:
\[
2^6
\]