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, we need to evaluate expressions by applying the rules of exponents and the effects of parentheses on negative numbers:

• $(-3)^2$: When a negative number is squared, the result is positive. So, $(-3)^2$ means $-3 \times -3 = 9$.
• $-(-3)^2$: This means $-1 \times (-3 \times -3)$ because squaring a number negates the negative sign inside parentheses, resulting in $-9$.
• $-(3)^2$: This equals $-1 \times (3 \times 3) = -9$, as the negative sign is outside the squared value.
• $-3$: This is simply $-3$.

Only $(-3)^2$ equals 9, confirming it as the correct expression required by the problem.

Therefore, the solution to the problem is $(-3)^2$.

To solve this problem, we'll evaluate the expression $-(-1)^{80}$.

• Step 1: Evaluate $(-1)^{80}$.

Since the exponent 80 is an even number, by applying the rule for negative powers, $(-1)^{80} = 1$.

• Step 2: Apply the negation.

The expression is $-(-1)^{80}$, which simplifies to $-1$, because negating 1 results in $-1$.

Therefore, the solution to the problem is $-1$.