Simplify each expression.
$(-6^5{)}^{{}^5}$

• A. ${(-6)}^{25}$
• B. ${(-6)}^{10}$
• C. $6^{25}$
• D. ${(-6)}^5$

Answer: (A)

Verified step by step guidance

1. Recall the Power of a Product Rule, which states that for any numbers \(a\) and \(b\) and any exponent \(n\), \((ab)^n = a^n b^n\). This means you raise each factor inside the parentheses to the power outside.
2. Identify the base factors inside the parentheses and the exponent outside. For example, if you have \((xy)^3\), the base factors are \(x\) and \(y\), and the exponent is \(3\).
3. Apply the rule by raising each base factor to the exponent separately: \(x^3\) and \(y^3\).
4. Rewrite the expression as the product of these powers: \(x^3 y^3\).
5. If needed, simplify each term further by applying other exponent rules or by calculating powers if the bases are numbers.