EXPONENTS WITH NEGATIVE BASES WORKSHEET

Problem 1

Evaluate :

-82

Problem 2 :

Evaluate :

(-8)2

Problem 3 :

Evaluate :

(-8)3

Problem 4 :

Evaluate :

3-2

Problem 5 :

Evaluate :

(-3/2)-2

Problem 6 :

Evaluate :

(-5/4)-3

Problem 7 :

Evaluate :

(-5-2⋅ (-3-4)

Problem 8 :

Evaluate :

(-3)-4/ (-2)-3

Problem 9 :

It is given that -a-1/3  =  3. Find the value of a. 

Problem 10 :

It is given that (-a)-1/3  =  4/3. Find the value of a. 

Detailed Answer Key

Problem 1 :

Evaluate :

-82

Solution :

= -82

= - 8 ⋅ 8

= - 64

Problem 2 :

Evaluate :

(-8)2

Solution :

= (-8)(-8)

= 64

Problem 3 :

Evaluate :

(-8)3

Solution :

= (-8)(-8)(-8)

= -512

Problem 4 :

Evaluate :

3-2

Solution :

= 3-2

= (1/3)2

Distribute the exponent to numerator and denominator.

= 1/ 32

= 1/9

Problem 5 :

Evaluate :

(-3/2)-2

Solution :

= (-3/2)-2

= (-2/3)2

Since the exponent is even, the negative sign inside the parentheses will become positive.

= (2/3)2

Distribute the exponent to numerator and denominator.

= 22/32

= 4/9

Problem 6 :

Evaluate :

(-5/4)-3

Solution :

= (-5/4)-3

= (-4/5)3

Since the exponent is odd, the negative sign inside the parentheses will remain same. 

Distribute the exponent to numerator and denominator. 

= -43/53

= -64/125

Problem 7 :

Evaluate :

(-5-2⋅ (-3-4)

Solution :

= (-5-2⋅ (-3-4)

= (-1/5)⋅ (-1/3)4

= (1/25)  (1/81)

= 1/2025

Problem 8 :

Evaluate :

(-3)-4/(-2)-3

Solution :

= (-3)-4/(-2)-3

= (-1/3)4/(-1/2)3

= (1/81)/(-1/8)

= (1/81) ⋅ (-8/1)

= -8/81

Problem 9 :

It is given that -a-1/3  =  3. Find the value of a.

Solution :

-a1/3 = 3

Multiply each side by -1.

a1/3 = -3

a = (-3)3/1

= (-3)3

= (-3)(-3)(-3)

= -27

Problem 10 :

It is given that (-a)-1/3  =  4/3. Find the value of a.

Solution :

(-a)-1/3 = 4/3

-a = (4/3)-3/1

-a = (4/3)-3

-a = (3/4)3

Distribute the exponent to numerator and denominator.

-a = 33/43

-a = 27/64

Multiply each side by -1.

a = - 27/64

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