Question
Simplify using the Product Rule: 2^4 × 2^2 × 2^3
Answers
Answered by
GPT-4o mini
To simplify the expression \( 2^4 \times 2^2 \times 2^3 \) using the Product Rule of exponents, we can apply the rule that states:
\[
a^m \times a^n = a^{m+n}
\]
Here, we can combine the exponents of the same base (which is 2 in this case):
\[
2^4 \times 2^2 \times 2^3 = 2^{4+2+3}
\]
Now, we calculate the sum of the exponents:
\[
4 + 2 + 3 = 9
\]
So, we have:
\[
2^4 \times 2^2 \times 2^3 = 2^9
\]
Thus, the simplified expression is:
\[
\boxed{2^9}
\]
\[
a^m \times a^n = a^{m+n}
\]
Here, we can combine the exponents of the same base (which is 2 in this case):
\[
2^4 \times 2^2 \times 2^3 = 2^{4+2+3}
\]
Now, we calculate the sum of the exponents:
\[
4 + 2 + 3 = 9
\]
So, we have:
\[
2^4 \times 2^2 \times 2^3 = 2^9
\]
Thus, the simplified expression is:
\[
\boxed{2^9}
\]