Answer :
Let's solve which option is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
First, let's find the value of [tex]\(\left(\frac{4}{5}\right)^6\)[/tex]. When you raise a fraction to a power, you raise both the numerator and the denominator to that power:
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
The calculation shows that:
- [tex]\(4^6\)[/tex] is equal to 4096.
- [tex]\(5^6\)[/tex] is equal to 15625.
So, the fraction [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] simplifies to:
[tex]\[
\frac{4096}{15625}
\][/tex]
Now let's evaluate each option:
Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
This option would equal [tex]\(6 \times 0.8 = 4.8\)[/tex], which is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option B: [tex]\(\frac{24}{30}\)[/tex]
This can be simplified to [tex]\(\frac{4}{5} = 0.8\)[/tex], which is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option C: [tex]\(\frac{4^6}{5}\)[/tex]
Here, you have:
- The numerator is [tex]\(4^6 = 4096\)[/tex].
- The denominator is [tex]\(5\)[/tex].
This results in [tex]\(\frac{4096}{5} = 819.2\)[/tex], which is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Based on the evaluations above, none of the given options match [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] correctly.
First, let's find the value of [tex]\(\left(\frac{4}{5}\right)^6\)[/tex]. When you raise a fraction to a power, you raise both the numerator and the denominator to that power:
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
The calculation shows that:
- [tex]\(4^6\)[/tex] is equal to 4096.
- [tex]\(5^6\)[/tex] is equal to 15625.
So, the fraction [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] simplifies to:
[tex]\[
\frac{4096}{15625}
\][/tex]
Now let's evaluate each option:
Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
This option would equal [tex]\(6 \times 0.8 = 4.8\)[/tex], which is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option B: [tex]\(\frac{24}{30}\)[/tex]
This can be simplified to [tex]\(\frac{4}{5} = 0.8\)[/tex], which is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option C: [tex]\(\frac{4^6}{5}\)[/tex]
Here, you have:
- The numerator is [tex]\(4^6 = 4096\)[/tex].
- The denominator is [tex]\(5\)[/tex].
This results in [tex]\(\frac{4096}{5} = 819.2\)[/tex], which is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Based on the evaluations above, none of the given options match [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] correctly.
