Which of the following is an equivalent expression to (1 - x/(x+blah))^20?

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Multiple Choice

Which of the following is an equivalent expression to (1 - x/(x+blah))^20?

The key idea is to rewrite the inner part with a common denominator. Write 1 as (x+blah)/(x+blah). Then 1 - x/(x+blah) = (x+blah)/(x+blah) - x/(x+blah) = [ (x+blah) - x ] / (x+blah) = blah/(x+blah). So the whole expression becomes [blah/(x+blah)]^20. That's why the equivalent form is (blah/(x+blah))^20. The other forms change the value: removing the exponent 20 would give just the base, changing the exponent to 8 changes the power, and altering the denominator to x+blah+1 changes the fraction altogether.

The key idea is to rewrite the inner part with a common denominator. Write 1 as (x+blah)/(x+blah). Then

1 - x/(x+blah) = (x+blah)/(x+blah) - x/(x+blah) = [ (x+blah) - x ] / (x+blah) = blah/(x+blah).

So the whole expression becomes [blah/(x+blah)]^20. That's why the equivalent form is (blah/(x+blah))^20. The other forms change the value: removing the exponent 20 would give just the base, changing the exponent to 8 changes the power, and altering the denominator to x+blah+1 changes the fraction altogether.

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