# Powers of negative numbers - Examples, Exercises and Solutions

## Exponentiation of Negative Numbers

### Negative number raised to an even power

Raising any negative number to an even power will result in a positive outcome.
When $n$ is even:
$(-x)^n=x^n$

### Negative number raised to an odd power

Raising any negative number to an odd power will result in a negative outcome.
When $n$ is odd:
$(-x)^n=-(x)^n$

### What is the difference between a power that is inside parentheses and one that is outside of them?

When the exponent is outside the parentheses - it applies to everything inside them.
When the exponent is inside the parentheses - it applies only to its base and not to the minus sign that precedes it.

## Practice Powers of negative numbers

### Exercise #1

$(-2)^7=$

### Video Solution

$-128$

### Exercise #2

$-(2)^2=$

### Video Solution

$-4$

### Exercise #3

$(-8)^2=$

### Video Solution

$64$

### Exercise #4

$9=$

### Video Solution

$(-3)^2$

### Exercise #5

$-(-1)^{80}=$

### Video Solution

$-1$

### Exercise #1

$-6^2=$

### Video Solution

$-36$

### Exercise #2

$(-1)^{99}=$

### Video Solution

$-1$

### Exercise #3

$-(-1)^{100}=$

### Video Solution

$-1$

### Exercise #4

$-(-2)^3=$

### Video Solution

$8$

### Exercise #5

$-(-6)^2=$

### Video Solution

$-36$

### Exercise #1

$-(7)^2=$

### Video Solution

$-49$

### Exercise #2

$64=$

### Video Solution

$(-8)^2$

### Exercise #3

$8=$

### Video Solution

$-(-2)^3$

### Exercise #4

$49=$

### Video Solution

$(-7)^2$

### Exercise #5

$36=$

### Video Solution

$(-6)^2$