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Chapter 1: Problem 108

Simplify each expression. $$3^{3}+(3-1)^{3}$$

Short Answer

Expert verified
The simplified expression equals 35.

Step by step solution

01

Solve the Exponents

In this step, the numbers raised to the third power are being solved. This means that \(3^{3}\) is calculated as '3 times 3 times 3', which equals 27. Similarly, \(1^{3}\) (which results from the term \(3 - 1\)) is 1.
02

Subtract Inside the Parentheses

The subtraction operation inside the parentheses is performed next, according to the order of operations. So \(3-1\) equals 2, and the expression becomes \(27+2^{3}\).
03

Solve the Remaining Exponent

Solve for the remaining exponent, \(2^{3}\), which equals 8.
04

Add the Results

In the final step, the results of \(27\) and \(8\) are added together to get the final answer.

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