Answer :
To find which of the given options is equal to [tex]\((\frac{4}{5})^6\)[/tex], we need to evaluate each option one by one.
1. Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
Calculate this expression:
[tex]\[
6 \cdot \frac{4}{5} = \frac{24}{5} = 4.8
\][/tex]
2. Option B: [tex]\(\frac{24}{30}\)[/tex]
Simplify this fraction:
[tex]\[
\frac{24}{30} = \frac{4}{5} = 0.8
\][/tex]
3. Option C: [tex]\(\frac{4^6}{5^6}\)[/tex]
Both the numerator and denominator need to be calculated:
[tex]\[
4^6 = 4096 \quad \text{and} \quad 5^6 = 15625
\][/tex]
So,
[tex]\[
\frac{4^6}{5^6} = \frac{4096}{15625} \approx 0.262144
\][/tex]
4. Option D: [tex]\(\frac{4^6}{5}\)[/tex]
Calculate this value:
[tex]\[
\frac{4^6}{5} = \frac{4096}{5} = 819.2
\][/tex]
Now, let's compare these results with the value [tex]\((\frac{4}{5})^6\)[/tex]:
- [tex]\((\frac{4}{5})^6 \approx 0.262144\)[/tex]
Comparing all options, we can clearly see that Option C: [tex]\(\frac{4^6}{5^6}\)[/tex] is approximately equal to [tex]\((\frac{4}{5})^6\)[/tex]. Therefore, Option C is the correct choice.
1. Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
Calculate this expression:
[tex]\[
6 \cdot \frac{4}{5} = \frac{24}{5} = 4.8
\][/tex]
2. Option B: [tex]\(\frac{24}{30}\)[/tex]
Simplify this fraction:
[tex]\[
\frac{24}{30} = \frac{4}{5} = 0.8
\][/tex]
3. Option C: [tex]\(\frac{4^6}{5^6}\)[/tex]
Both the numerator and denominator need to be calculated:
[tex]\[
4^6 = 4096 \quad \text{and} \quad 5^6 = 15625
\][/tex]
So,
[tex]\[
\frac{4^6}{5^6} = \frac{4096}{15625} \approx 0.262144
\][/tex]
4. Option D: [tex]\(\frac{4^6}{5}\)[/tex]
Calculate this value:
[tex]\[
\frac{4^6}{5} = \frac{4096}{5} = 819.2
\][/tex]
Now, let's compare these results with the value [tex]\((\frac{4}{5})^6\)[/tex]:
- [tex]\((\frac{4}{5})^6 \approx 0.262144\)[/tex]
Comparing all options, we can clearly see that Option C: [tex]\(\frac{4^6}{5^6}\)[/tex] is approximately equal to [tex]\((\frac{4}{5})^6\)[/tex]. Therefore, Option C is the correct choice.
