Respuesta :
Option D
The fraction equal to the fraction [tex]\left(\frac{4}{5}\right)^{6}[/tex] is [tex]\frac{4^{6}}{5^{6}}[/tex]
Solution:
Need to check which of the given option is equal to fraction [tex]\left(\frac{4}{5}\right)^{6}[/tex]
Lets look at one of the law of exponents which is useful in our case
[tex]\text { For any fraction }\left(\frac{a}{b}\right)^{m}=\frac{a^{m}}{b^{m}} \text { where } a \text { and } b \text { are integers }[/tex]
In our case a = 4 and b = 5 and m = 6
On applying the above law of exponents we get
[tex]\left(\frac{4}{5}\right)^{6}=\frac{4^{6}}{5^{6}}[/tex]
Also we can do it in another way:
[tex]\left(\frac{4}{5}\right)^{6}=\frac{4}{5} \times \frac{4}{5} \times \frac{4}{5} \times \frac{4}{5} \times \frac{4}{5} \times \frac{4}{5}=\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4}{5 \times 5 \times 5 \times 5 \times 5 \times 5}=\frac{4^{6}}{5^{6}}[/tex]
Hence we can say that [tex]\left(\frac{4}{5}\right)^{6}=\frac{4^{6}}{5^{6}}[/tex] and correct option is D
