Answer :
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.
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.
