Question
Two to the fourth power times two to the third power and parentheses times two to the second power over to to the eighth power equals what
Answers
GPT-4o mini
To solve the expression \( \frac{(2^4 \times 2^3 \times 2^2)}{2^8} \), we can simplify it step-by-step using the properties of exponents.
First, we can combine the exponents in the numerator:
\[
2^4 \times 2^3 \times 2^2 = 2^{4+3+2} = 2^9
\]
Now we can rewrite the entire expression as:
\[
\frac{2^9}{2^8}
\]
Using the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \):
\[
\frac{2^9}{2^8} = 2^{9-8} = 2^1
\]
Thus, this simplifies to:
\[
2^1 = 2
\]
Therefore, the final result is:
\[
\boxed{2}
\]
First, we can combine the exponents in the numerator:
\[
2^4 \times 2^3 \times 2^2 = 2^{4+3+2} = 2^9
\]
Now we can rewrite the entire expression as:
\[
\frac{2^9}{2^8}
\]
Using the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \):
\[
\frac{2^9}{2^8} = 2^{9-8} = 2^1
\]
Thus, this simplifies to:
\[
2^1 = 2
\]
Therefore, the final result is:
\[
\boxed{2}
\]