help i need it What is the value of $(2x^3) \div (2x)^3$ when $x = 2007$? Express your answer as a common fraction.

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plz help What is the value of $(2x^3) \div (2x)^3$ when $x = 2007$? Express your answer as a common fraction.

Guest Jun 18, 2020

MaxWong · Answer 1 · 2020-06-18T06:55:24

+9519

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You can first simplify the expression before substituting x = 2007.

Hint: The expression is constant for any values of x. That means no matter what x is, it always gives the same value.

MaxWong Jun 18, 2020

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i did that but it seems to get more complicated can you show me how you did the entire thing step by step, it would be greatly appreciated thank you!

Guest Jun 18, 2020

+9519

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The idea:

By law of indices, $(2x)^3 = 2^3 x^3 = 8x^3$

The denominator is 8x³ and the numerator is 2x³.

Now it is obvious that we can rewrite 8x³ as 4(2x³) and cross out 2x³.

Simplifying gives 1/4.

MaxWong Jun 18, 2020