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jmc

algebra junior

Problem

What is the value of

(2 x^{3}) \div (2 x)^{3}

when

x = 2007

? Express your answer as a common fraction.

Solution

We have

\frac{2 x ^{3}}{( 2 x ) ^{3}} = \frac{2 x ^{3}}{2 ^{3} x ^{3}} = \frac{2}{2 ^{3}} \cdot \frac{x ^{3}}{x ^{3}} = \frac{1}{4}

.

Final answer

\frac14