Powers of Negative Numbers Practice Problems and Solutions

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 $-128$.

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 this problem, let's evaluate both given expressions to determine which results in 8.

• Step 1: Evaluate $(-2)^3$:
  $(-2)^3 = (-2) \times (-2) \times (-2)$.
  Multiplying across: $(-2) \times (-2) = 4$, and then $4 \times (-2) = -8$.
  Thus, $(-2)^3 = -8$.
• Step 2: Evaluate $-(-2)^3$:
  First, calculate $(-2)^3$ again: We already know $(-2)^3 = -8$.
  Now, apply the negative sign: $-(-8) = 8$.

Therefore, the expression that equals $8$ is $-(-2)^3$.

Thus, the correct expression that evaluates to 8 is $-(-2)^3$.

To solve this problem, we'll need to carefully consider the placement of parentheses and the order of operations when dealing with negative numbers and exponentiation:

• Step 1: Examine the given expression $(-4)^2$. This indicates squaring the entire negative four, which results in $16$.
• Step 2: Now, examine $-(-4)^2$ paying close attention to the negative sign in front. $(-4)^2$ again results in $16$, but placing a minus before it changes its sign to $-16$.

Let's analyze each possible choice:

• For choice 1: The expression is $-(-4)^2$. Calculating $(-4)^2$ gives $16$, and applying the negative sign outside results in the expression value of $-16$.
• For choice 2: The expression is $(-4)^2$, calculated to give $16$.

Therefore, the expression that correctly equals $-16$ is choice 1, represented by $-(-4)^2$.

The correct answer is choice 1: $-(-4)^2$.