Rewrite the product as an exponential expression.
$\left(\frac{2}{9}\right)\times \left(\frac{2}{9}\right)\times \left(\frac{2}{9}\right)\times \left(\frac{2}{9}\right)\times \left(\frac{2}{9}\right)$

• A. $5^{\left(\frac{2}{9}\right)}$
• B. ${\left(\frac{2}{9}\right)}^{\frac{2}{9}}$
• C. $5^5$
• D. ${\left(\frac{2}{9}\right)}^5$

Answer: (D)

Verified step by step guidance

1. Identify the repeated factor in the product. Here, the factor \(\left(\frac{2}{9}\right)\) is multiplied by itself 5 times.
2. Recall the definition of an exponential expression: multiplying the same base repeatedly is expressed as the base raised to the power of the number of times it is multiplied.
3. Write the product \(\left(\frac{2}{9}\right) \times \left(\frac{2}{9}\right) \times \left(\frac{2}{9}\right) \times \left(\frac{2}{9}\right) \times \left(\frac{2}{9}\right)\) as an exponential expression with base \(\frac{2}{9}\) and exponent 5.
4. Express this as \(\left(\frac{2}{9}\right)^5\), which means \(\frac{2}{9}\) multiplied by itself 5 times.
5. This exponential form simplifies the notation and clearly shows the repeated multiplication of the fraction.