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 real number exponent.
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 \$3x^{2}\(; for \)x^5\(, the derivative is \)5x^{4}$, and so on.
4. If the expression includes coefficients (numbers multiplied by the power terms), remember to keep the coefficients as they are and multiply them by the exponent when applying the Power Rule.
5. After applying the Power Rule to all terms, write the simplified expression with the new exponents and coefficients. This will be the derivative or simplified form of the original expression using the Power Rule.