Powers Special Cases Practice - Negative Exponents & Zero Power

Let's solve the problem step by step using the Zero Exponent Rule, which states that any non-zero number raised to the power of 0 is equal to 1.

• Consider the expression: $100^0$.
• According to the Zero Exponent Rule, if we have any non-zero number, say $a$, then $a^0 = 1$.
• Here, $a = 100$ which is clearly a non-zero number, so following the rule, we find that:
• $100^0 = 1$.

Therefore, the expression $100^0$ is equivalent to 1.

We use the zero exponent rule.

$X^0=1$We obtain

$112^0=1$Therefore, the correct answer is option C.

To solve this problem, we need to find the value of $4^0$.

• Step 1: According to the properties of exponents, for any non-zero number $a$, the zero power $a^0$ is always equal to 1.

• Step 2: Here, our base is 4, which is a non-zero number.

• Step 3: Applying the zero exponent rule, we find:

$4^0 = 1$

Thus, the answer to the question is $1$, corresponding to choice 3.

To solve the problem, $(\frac{1}{8})^0$, we utilize the Zero Exponent Rule, which states that any non-zero number raised to the power of zero equals $1$.

Here's a step-by-step explanation:

• Step 1: Identify the base and ensure it is non-zero. In this case, the base is $\frac{1}{8}$, which is indeed non-zero.
• Step 2: Apply the Zero Exponent Rule. According to this rule, $\left(\frac{1}{8}\right)^0 = 1$.
• Step 3: Conclude the result: The expression evaluates to $1$.

Therefore, the correct answer to the problem $(\frac{1}{8})^0$ is $1$.

To solve this problem, we'll follow these steps:

• Step 1: Recognize that the base of the exponent is 1.
• Step 2: Apply the Zero Exponent Rule.
• Step 3: Verify the result is consistent with mathematical rules.

Now, let's work through each step:
Step 1: We have the expression $1^0$, where 1 is the base.
Step 2: According to the Zero Exponent Rule, any non-zero number raised to the power of zero is equal to 1. Hence, $1^0 = 1$.
Step 3: Verify: The base 1 is indeed non-zero, confirming that the zero exponent rule applies.

Therefore, the value of $1^0$ is $1$.