SIMPLIFYING EXPONENTIAL EXPRESSIONS

Problem 1 :

Evaluate: 4² - [6 ÷ (-2)]³

Solution:

= 4² - [6 ÷ (-2)]³

= 16 - [-3]³

= 16 - (-27)

= 16 + 27

= 43

Problem 2 :

Simplify, then evaluate.

(-2)⁵ × (-2)⁷ ÷ (-2)⁶

Solution:

= (-2)⁵ × (-2)⁷ ÷ (-2)⁶

= (-32) × (-128) ÷ (64)

= (-32) × (-2)

= 64

Problem 3 :

Simplify, then evaluate.

Solution:

Problem 4 :

(6)⁰ + [8 ÷ (-2)]² - 5

Solution:

= (6)⁰ + [8 ÷ (-2)]² - 5

= 1 + [-4]² - 5 

= 1 + 16 - 5

= 17 - 5

= 12

Problem 5 :

Simplify, then evaluate.

Solution:

Problem 6 :

Simplify, then evaluate.

(4⁹ ÷ 4⁶)² - (2⁸ ÷ 2⁶)²

Solution: 

= (4⁹ ÷ 4⁶)² - (2⁸ ÷ 2⁶)²

= (4^9-6)² - (2^8-6)²

= (4³)² - (2²)²

= 4⁶ - 2⁴

= 4096 - 16

= 4080

Problem 7 :

Evaluate: 5(3)³ - 3(-5)³

Solution:

= 5(3)³ - 3(-5)³

= 5(27) - 3(-125)

= 135 + 375

= 510

Problem 8 :

Evaluate:

Solution:

Problem 9 :

3³ × 3⁴ ÷ 3⁶

Solution:

= 3³ × 3⁴ ÷ 3⁶

= (3³⁺⁴) ÷ 3⁶

= 3^7-6

= 3¹

= 3

Problem 10 :

(3² × 3³)²

Solution:

= (3² × 3³)²

= (3²⁺³)²

= (3⁵)²

= 3¹⁰

= 59049

Problem 11 :

Simplify, then evaluate. Show your work.

Solution: