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

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Full solution

Q. Evaluate. Write your answer as a fraction or whole number.\newline(23)3(\frac{2}{3})^3 = _____
  1. Understand the problem: Understand the problem.\newlineWe need to calculate the value of the fraction 23\frac{2}{3} raised to the power of 33.
  2. Apply the exponent: Apply the exponent to the fraction.\newlineWhen a fraction is raised to an exponent, both the numerator and the denominator are raised to that exponent.\newline(23)3=(2333)(\frac{2}{3})^3 = (\frac{2^3}{3^3})
  3. Calculate the numerator: Calculate the numerator.\newline232^3 means 22 multiplied by itself 33 times.\newline23=2×2×2=82^3 = 2 \times 2 \times 2 = 8
  4. Calculate the denominator: Calculate the denominator.\newline333^3 means 33 multiplied by itself 33 times.\newline33=3×3×3=273^3 = 3 \times 3 \times 3 = 27
  5. Write the fraction: Write the fraction with the calculated numerator and denominator.\newline(23)3=827(\frac{2}{3})^3 = \frac{8}{27}

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