Simplify the following expression.
Mathematics
hutchisonlexie
Question
Simplify the following expression.
1 Answer

1. User Answers 19allenethm
Answer:
C. [tex]\frac{1}{64}[/tex]
Stepbystep explanation:
First, we can set up our expression as such
[tex]\frac{4^{\frac{11}{3} } }{4^{\frac{2}{3} } }[/tex]
When you divide two numbers with the same base and different powers, all you do is subtract the lower power from the upper.
In this case the powers are [tex]\frac{11}{3}[/tex] and [tex]\frac{2}{3}[/tex]
This means that the power would be
[tex]\frac{11}{3}(\frac{2}{3})\\\\\frac{11}{3}+\frac{2}{3}\\\\\frac{9}{3}[/tex]
Now we can put this power back on its base and then simplify.
[tex]4^{\frac{9}{3} } \\\\4^{3} \\\\\frac{1}{4^{3} } \\\\\frac{1}{64}[/tex]