Powers Special Cases Practice - Negative Exponents & Zero Power

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

• Step 1: Calculate $(2)^2$
• Step 2: Apply the negative sign

Now, let's work through each step:
Step 1: Calculate $(2)^2$. This is equal to $2 \times 2 = 4$.
Step 2: Apply the negative sign: The expression $-(2)^2$ now becomes $-4$.

Therefore, the value of the expression $-(2)^2$ is $-4$.

This matches choice 4, which is $-4$.

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.

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 $1$.

When we have a negative number raised to a power, the location of the minus sign is very important.

If the minus sign is inside or outside the parentheses, the result of the exercise can be completely different.

When the minus sign is inside the parentheses, our exercise will look like this:

(-8)*(-8)=

Since we know that minus times minus is actually plus, the result will be positive:

(-8)*(-8)=64

To solve for $(-2)^7$, follow these steps:

• Step 1: Identify the base and the exponent given in the expression, which are $-2$ and $7$, respectively.
• Step 2: Recognize that since the exponent is $7$, which is an odd number, the result of the power will remain negative: $(-2)^7$ will be $- (2^7)$.
• Step 3: Compute $2^7$. This involves multiplying $2$ by itself $7$ times:
  $2 \times 2 = 4$
  $4 \times 2 = 8$
  $8 \times 2 = 16$
  $16 \times 2 = 32$
  $32 \times 2 = 64$
  $64 \times 2 = 128$
  Thus, $2^7 = 128$.
• Step 4: Apply the negative sign to the result of $2^7$, resulting in $-128$.

Therefore, the value of $(-2)^7$ is $-128$.