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Evaluate. Write your answer as a fraction or whole number.\newline(14)4=(\frac{1}{4})^4 = _____

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Full solution

Q. Evaluate. Write your answer as a fraction or whole number.\newline(14)4=(\frac{1}{4})^4 = _____
  1. Given Expression: We are given the expression (14)4(\frac{1}{4})^4. This means we need to multiply 14\frac{1}{4} by itself four times.
  2. Calculate (14)4(\frac{1}{4})^4: To calculate (14)4(\frac{1}{4})^4, we multiply the numerator by itself four times and the denominator by itself four times.(14)4=(1×1×1×14×4×4×4)(\frac{1}{4})^4 = (\frac{1\times1\times1\times1}{4\times4\times4\times4})
  3. Perform Multiplication: Perform the multiplication for both the numerator and the denominator.\newline(1×1×1×1)/(4×4×4×4)=1/256(1\times1\times1\times1)/(4\times4\times4\times4) = 1/256
  4. Check Correctness: Check to ensure that the multiplication was done correctly. The numerator 11 multiplied by itself any number of times will always be 11. The denominator 44 multiplied by itself four times is 4×4×4×44\times4\times4\times4 which is 16×1616\times16, and that equals 256256.

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