Answer: Choice D [tex]\frac{4^6}{5^6}[/tex]
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Explanation:
The rule is
[tex]\left(\frac{a}{b}\right)^c = \frac{a^c}{b^c}[/tex]
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
[tex]\left(\frac{4}{5}\right)^6 = \left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)\\\\\left(\frac{4}{5}\right)^6 = \frac{4*4*4*4*4*4}{5*5*5*5*5}\\\\\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}\\[/tex]
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.
