Question

What is the equivalent numerical value of the expression 2=^4x2^7
? Enter the simplified number (with no exponents) in the box.

Answer

Answer 1

To simplify the expression \( 2 = 4 \times 2^7 \), we first need to express \( 4 \) in terms of base \( 2 \):

\[
4 = 2^2
\]

Now, substitute \( 4 \) with \( 2^2 \) in the expression:

\[
4 \times 2^7 = 2^2 \times 2^7
\]

Now we can use the property of exponents that states \( a^m \times a^n = a^{m+n} \):

\[
2^2 \times 2^7 = 2^{2+7} = 2^9
\]

Now we have:

\[
2 = 2^9
\]

To find the equivalent numerical value of \( 2^9 \):

\[
2^9 = 512
\]

So, the simplification results in:

\[
\boxed{512}
\]