Powers of Negative Numbers Practice Problems and Solutions

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 $-4$.

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 $-128$.

The given problem asks us to evaluate the expression $-(7)^2$. To solve this, we must correctly handle the operations of exponentiation and negation.

Firstly, examine $(7)^2$:
- $(7)^2$ means multiplying 7 by itself.
- Calculating this gives: $7 \times 7 = 49$.

Next, apply the negative sign to the result:
- The expression $-(7)^2$ indicates that we apply the negative sign to the result of $(7)^2$.
- Therefore, multiply the result by $-1$:
$-1 \times 49 = -49$.

Thus, the correct evaluation of the expression is $-49$.

Thus, the solution to this problem is $-49$.

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

• Step 1: Recognize the order of operations.
• Step 2: Evaluate the exponent first before applying any operations outside the exponent.
• Step 3: Apply the negative sign to the result of the squared value.

Now, let's work through each step:
Step 1: The expression $-6^2$ involves squaring the number 6. According to the order of operations, we compute exponents before multiplying by -1.
Step 2: This means we first calculate $6^2$, which is equal to 36.
Step 3: After evaluating the square, apply the negative sign: $-6^2 = -(6^2) = -36$.

Therefore, the solution to the problem is $-36$.