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Evaluate. Write your answer as a fraction or whole number.\newline(23)4(\frac{2}{3})^4 = _____

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Full solution

Q. Evaluate. Write your answer as a fraction or whole number.\newline(23)4(\frac{2}{3})^4 = _____
  1. Identify Base and Exponent: Identify the base and the exponent of (23)4(\frac{2}{3})^4.\newlineIn (23)4(\frac{2}{3})^4, 23\frac{2}{3} is the base raised to the exponent 44.\newlineBase: 23\frac{2}{3}\newlineExponent: 44
  2. Choose Expanded Form: Choose the expanded form of (23)4(\frac{2}{3})^4(23)4(\frac{2}{3})^4 means (23)(\frac{2}{3}) is multiplied by itself 44 times. Expanded Form: (23×23×23×23)(\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3})
  3. Multiply Numerators and Denominators: (23)4=(23×23×23×23)(\frac{2}{3})^4 = (\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3}) Multiply the numerators and the denominators separately to write in simplest form. (23)4=(2×2×2×2)/(3×3×3×3)=1681(\frac{2}{3})^4 = (2 \times 2 \times 2 \times 2) / (3 \times 3 \times 3 \times 3) = \frac{16}{81} Simplest form: 1681\frac{16}{81}

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