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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. Identify base and exponent: Identify the base and the exponent in the expression (14)4\left(\frac{1}{4}\right)^4.\newlineBase: 14\frac{1}{4}\newlineExponent: 44
  2. Understanding exponentiation of fractions: Understand that raising a fraction to an exponent means multiplying the fraction by itself as many times as the value of the exponent. (14)4(\frac{1}{4})^4 means 14\frac{1}{4} multiplied by itself 44 times.
  3. Write expanded form: Write the expanded form of (14)4\left(\frac{1}{4}\right)^4.\newlineExpanded Form: 14×14×14×14\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}
  4. Multiply numerators and denominators: Multiply the numerators and the denominators separately. \newline(14)4=1×1×1×14×4×4×4\left(\frac{1}{4}\right)^4 = \frac{1 \times 1 \times 1 \times 1}{4 \times 4 \times 4 \times 4}
  5. Calculate product of numerators and denominators: Calculate the product of the numerators and the product of the denominators.\newline1×1×1×1=11 \times 1 \times 1 \times 1 = 1\newline4×4×4×4=2564 \times 4 \times 4 \times 4 = 256
  6. Combine products for final answer: Combine the products to get the final answer. \newline(14)4=1256\left(\frac{1}{4}\right)^4 = \frac{1}{256}

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