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 nn is even:
(x)n=xn(-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 nn is odd:
(x)n=(x)n(-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= (-2)^7=

Video Solution

Answer

128 -128

Exercise #2

(2)2= -(2)^2=

Video Solution

Answer

4 -4

Exercise #3

(8)2= (-8)^2=

Video Solution

Answer

64 64

Exercise #4

9= 9=

Video Solution

Answer

(3)2 (-3)^2

Exercise #5

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

Video Solution

Answer

1 -1

Exercise #1

62= -6^2=

Video Solution

Answer

36 -36

Exercise #2

(1)99= (-1)^{99}=

Video Solution

Answer

1 -1

Exercise #3

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

Video Solution

Answer

1 -1

Exercise #4

(2)3= -(-2)^3=

Video Solution

Answer

8 8

Exercise #5

(6)2= -(-6)^2=

Video Solution

Answer

36 -36

Exercise #1

(7)2= -(7)^2=

Video Solution

Answer

49 -49

Exercise #2

64= 64=

Video Solution

Answer

(8)2 (-8)^2

Exercise #3

8= 8=

Video Solution

Answer

(2)3 -(-2)^3

Exercise #4

49= 49=

Video Solution

Answer

(7)2 (-7)^2

Exercise #5

36= 36=

Video Solution

Answer

(6)2 (-6)^2

Topics learned in later sections

  1. Exponents - Special Cases
  2. Zero Exponent Rule
  3. Negative Exponents