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.

= 1² / 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)² ⋅ (-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 :

-a^1/3 = 3

Multiply each side by -1.

a^1/3 = -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

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.