Mathematics

Question

Simplify the following expression.
Simplify the following expression.

1 Answer

  • Answer:

    C. [tex]\frac{1}{64}[/tex]

    Step-by-step 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]

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