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. Identify the expression involving exponents that you need to simplify or differentiate using the Power Rule. The Power Rule typically applies to expressions of the form \(x^n\), where \(n\) is a any real number.
2. Recall the Power Rule formula: if you have \(x^n\), then its derivative with respect to \(x\) is given by \(\frac{d}{dx} x^n = n \cdot x^{n-1}\). This means you multiply by the exponent and then subtract one from the exponent.
3. Apply the Power Rule to each term in the expression separately if there are multiple terms with exponents. For example, for \(x^3\), the derivative is \$3 \cdot x^{2}$.
4. Simplify the resulting expression by performing any multiplication and rewriting the powers clearly.
5. If the problem involves simplifying expressions with exponents (not derivatives), use the Power Rule for exponents: when multiplying powers with the same base, add the exponents (\(x^a \cdot x^b = x^{a+b}\)), and when raising a power to another power, multiply the exponents (\((x^a)^b = x^{a \cdot b}\)).