Question

Please help ! I don’t understand:((

Answer 1

Answer: Choice D
`(4^6)/(5^6)`

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Step-by-step explanation:

The rule is

`\left((a)/(b)\right)^c = (a^c)/(b^c)`

Basically we raise each part of the fraction to the outer exponent. In this case, a = 4, b = 5 and c = 6.

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The outer exponent c = 6 tells us how many copies of (a/b) we are multiplying together. So we are multiplying 6 copies of (4/5) together like so

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

For larger values of c, it's easiest to use the formula directly instead of expand things out like what is shown above. I recommend trying out small values of c such as c = 2 or c = 3.

Answer 2

4^6 / 5^6

Step-by-step explanation:

We know that (a/b) ^c = a^c / b^c

(4/5) ^6 = 4^6 / 5^6