Certainly! Let's determine the value of the expression \( 64^{40} \):
The expression we need to evaluate is:
[tex]\[ 64^{40} \][/tex]
Here, \( 64 \) is raised to the power of \( 40 \).
To understand how large this number is, let's consider the base \( 64 \):
- \( 64 \) is \( 2^6 \).
So, we can rewrite \( 64^{40} \) as:
[tex]\[ (2^6)^{40} \][/tex]
Using properties of exponents, we know that \( (a^m)^n = a^{m \cdot n} \). Applying this property, we have:
[tex]\[ (2^6)^{40} = 2^{6 \cdot 40} = 2^{240} \][/tex]
This simplifies to \( 2^{240} \), which is an extremely large number.
Let’s compare this with the given options:
A. 42\
B. 16\
C. 2\
D. 8
None of these options represent the value \( 2^{240} \), as they are all very small compared to this vast number. The exact value calculated for \( 64^{40} \) is:
[tex]\[ 1766847064778384329583297500742918515827483896875618958121606201292619776 \][/tex]
Therefore, the value of [tex]\( 64^{40} \)[/tex] does not match any of the provided options. Hence, the correct answer is that none of the given options (A, B, C, or D) is correct.
