Simplify each expression, but don’t evaluate.
${\left({100}^{26}\right)}^0$

• A. $0$
• B. ${100}^{26}$
• C. $100^0$
• D. $100^{\infty}$

Answer: (C)

Verified step by step guidance

1. Recognize the expression given: \(\left(100^{26}\right)^0\).
2. Recall the zero exponent rule, which states that any nonzero base raised to the zero power equals 1, i.e., \(a^0 = 1\) for \(a \neq 0\).
3. Apply the zero exponent rule to the entire expression \(\left(100^{26}\right)^0\), which means the whole quantity is raised to the zero power.
4. Understand that the exponent on the inside, 26, does not affect the zero exponent on the outside because the zero exponent applies to the entire quantity inside the parentheses.
5. Conclude that the simplified form of \(\left(100^{26}\right)^0\) is \$100^0\(, which by the zero exponent rule simplifies further to 1 (but since the problem says not to evaluate, leave it as \)100^0$).