Question

Calculate. 

A. (3 + 7)^3 

B. 5 + 4^4

Answer 1

A) The expression is (3 + 7)³.

Apply cube of the sum of two numbers formula: (a + b)³ = a³+ 3a²b + 3ab² + b³.

= 3³ + 3(3²)(7) + 3(3)(7²) + 7³

= 27 + 3(3²)(7) + 3(3)(7²) + 7³           [Evaluate power: 3³ = 27 ]

= 27 + 3(9)(7) + 3(3)(7²) + 7³            [Evaluate power: 3² = 9 ]

= 27 + 189 + 3(3)(7²) + 7³

= 27 + 189 + 3(3)(49) + 7³                [Evaluate power: 7² = 49 ]

= 27 + 189 + 441 + 7³

= 27 + 189 + 441 + 343                         [Evaluate power: 7³ = 343 ]

= 1000

Therefore (3 + 7)³ = 1000.

B) The expression is 5 + 4⁴.

= 5 + 256                                 [Evaluate power: 4⁴ = 256]

= 261.

Therefore 5 + 4⁴ = 261.

Answer 2

Order of Operations:

To simplify the expression follow the order of operations: (PEMDAS)

1.      Evaluate the expressions inside the Parenthesis/Brackets (P).

2.      Evaluate Powers/Exponents (E).

3.      Multiply and/or Divide in order from left to right (MD).

4.      Add and/or Subtract in order from left to right (AS).

(A). The expression is (3 + 7)³.

From PEMDAS rule, evaluate the expression inside the Parenthesis.

= (10)³.

Next evaluate powers.

= 10×10×10.

= 1000.

The value of (3 + 7)³ = 1000.