Which of the following is equal to the fraction below? (Apex)(4/5)^6A) 6(4/5)B) 24/30C)4^6/5D)4^6/5^6

Option DThe 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 = 6On 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