Simplify the expressions using the quotient to a power property.
${\left(\frac{8}{11}\right)}^2$

• A. $\frac{64}{121}$
• B. $\frac{8}{11}$
• C. $\frac{64}{11}$
• D. $\frac{8}{121}$

Answer: (A)

Verified step by step guidance

1. Identify the given expression: \(\left(\frac{8}{11}\right)^2\).
2. Recall the quotient to a power property, which states that \(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\), where \(a\), \(b\), and \(n\) are numbers.
3. Apply this property to the expression by raising both the numerator and the denominator to the power of 2: \(\frac{8^2}{11^2}\).
4. Calculate the powers separately: \$8^2\( and \)11^2$ (do not compute the final values here, just write the expressions).
5. Rewrite the expression as \(\frac{8^2}{11^2}\), which is the simplified form using the quotient to a power property.