Math Problem Statement

(6/3)^2-1-3^3

Solution

Let's break down the expression step by step:

(63)2133\left( \frac{6}{3} \right)^2 - 1 - 3^3

Step 1: Simplify the terms inside the parentheses

63=2\frac{6}{3} = 2

Step 2: Square the result

22=42^2 = 4

Step 3: Evaluate the powers

33=273^3 = 27

Step 4: Substitute the results into the expression

41274 - 1 - 27

Step 5: Simplify the expression

41=34 - 1 = 3 327=243 - 27 = -24

Thus, the final answer is:

24\boxed{-24}

Would you like further details on any step or have other questions?

Here are 5 related questions:

  1. What is the value of (8/4)2242(8/4)^2 - 2 - 4^2?
  2. How would you simplify (9/3)35+24(9/3)^3 - 5 + 2^4?
  3. What is the cube of 22 and how does it compare to 333^3?
  4. How would you approach evaluating expressions with exponents and parentheses?
  5. What are some common mistakes when working with order of operations?

Tip: Always follow the order of operations: parentheses, exponents, multiplication/division (left to right), addition/subtraction (left to right).

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Exponents
Arithmetic

Formulas

a^b (Exponentiation)
PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

Theorems

Order of Operations

Suitable Grade Level

Grades 6-8