Maths-
General
Easy

Question

2 to the power of 2 divided by n end exponent left parenthesis n-th root of 3 right parenthesis
If n is a positive integer, which of the following is the equivalent to the expression above?

  1. 3 to the power of 1 over n end exponent
  2. 18 to the power of 1 over n end exponent
  3. n-th root of 6
  4. n-th root of 12

The correct answer is: n-th root of 12


    given 2 to the power of 2 over n end exponent left parenthesis n-th root of 3 right parenthesis equals open parentheses 2 squared close parentheses to the power of 1 over n end exponent left parenthesis n-th root of 3 right parenthesis open curly brackets text  reason  end text x to the power of a over b end exponent equals open parentheses x to the power of a close parentheses to the power of 1 over b end exponent close curly brackets
    not stretchy rightwards double arrow left parenthesis 4 right parenthesis to the power of 1 over straight n end exponent left parenthesis straight n-th root of 3 right parenthesis equals left parenthesis 4 right parenthesis to the power of 1 over straight n end exponent left parenthesis 3 right parenthesis to the power of 1 over straight n end exponent stretchy left curly bracket text  reason  end text straight n-th root of straight x equals straight x to the power of 1 over straight n end exponent stretchy right curly bracket
    not stretchy rightwards double arrow left parenthesis 4 right parenthesis to the power of 1 over n end exponent left parenthesis 3 right parenthesis to the power of 1 over n end exponent equals left parenthesis 4 cross times 3 right parenthesis to the power of 1 over n end exponent equals 12 to the power of 1 over n end exponent open curly brackets text  reason  end text x to the power of a times y to the power of a equals left parenthesis x y right parenthesis to the power of a close curly brackets
    not stretchy rightwards double arrow 12 to the power of 1 over n end exponent equals n-th root of 12 open curly brackets text  reason  end text x to the power of 1 over n end exponent equals n-th root of x close curly brackets

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