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 \( \frac{2}{9} \) 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 base \( \frac{2}{9} \) with an exponent representing the number of factors, which is 5 in this case.
4. Express 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 \( \left(\frac{2}{9}\right)^5 \).
5. This exponential form compactly represents the original product and is the standard way to rewrite repeated multiplication.