Simplify the expressions using the quotient to a power property.
${\left(\frac{a}{-3}\right)}^4$

• A. $\frac{a^4}{-81}$
• B. $\(\frac{a^4}{81}\)$
• C. $\(\frac{a}{81}\)$
• D. $-\(\frac\)43a$

Answer: (B)

Verified step by step guidance

1. Identify the expression to simplify: \(\left(\frac{a}{-3}\right)^4\).
2. Apply the quotient to a power property, which states that \(\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}\), to rewrite the expression as \(\frac{a^4}{(-3)^4}\).
3. Calculate the denominator by raising \(-3\) to the 4th power, remembering that an even power makes the result positive, so \((-3)^4 = 3^4\).
4. Rewrite the expression as \(\frac{a^4}{3^4}\), which simplifies to \(\frac{a^4}{81}\) since \$3^4 = 81$.
5. Conclude that the simplified form of the original expression is \(\frac{a^4}{81}\).