Question

Which of the following is equal to the fraction below? (Apex)

(4/5)^6


A) 6(4/5)

B) 24/30

C)4^6/5

D)4^6/5^6

Answer 1

Option D

The fraction equal to the fraction
`\left((4)/(5)\right)^(6)` is
`(4^(6))/(5^(6))`

Solution:

Need to check which of the given option is equal to fraction
`\left((4)/(5)\right)^(6)`

Lets look at one of the law of exponents which is useful in our case

`\text { For any fraction }\left((a)/(b)\right)^(m)=(a^(m))/(b^(m)) \text { where } a \text { and } b \text { are integers }`

In our case a = 4 and b = 5 and m = 6

On applying the above law of exponents we get

`\left((4)/(5)\right)^(6)=(4^(6))/(5^(6))`

Also we can do it in another way:

`\left((4)/(5)\right)^(6)=(4)/(5) * (4)/(5) * (4)/(5) * (4)/(5) * (4)/(5) * (4)/(5)=(4 * 4 * 4 * 4 * 4 * 4)/(5 * 5 * 5 * 5 * 5 * 5)=(4^(6))/(5^(6))`

Hence we can say that
`\left((4)/(5)\right)^(6)=(4^(6))/(5^(6))` and correct option is D