Math Problem Statement

Use the order of operations to find the value of the following expression. 6 left parenthesis 3 minus 5 right parenthesis cubed minus 7 left parenthesis 4 minus 5 right parenthesis cubed Question content area bottom Part 1 6 left parenthesis 3 minus 5 right parenthesis cubed minus 7 left parenthesis 4 minus 5 right parenthesis cubedequals    enter your response here

Solution

Let's solve the expression using the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction).

Given:

6(3−5)3−7(4−5)36(3 - 5)^3 - 7(4 - 5)^3

Step 1: Simplify inside parentheses

6(−2)3−7(−1)36(-2)^3 - 7(-1)^3

Step 2: Apply exponents

=6(−8)−7(−1)= 6(-8) - 7(-1) =−48+7= -48 + 7

Step 3: Perform addition/subtraction

=−48+7=−41= -48 + 7 = -41

Final Answer:

−41\boxed{-41}

Would you like further details or a review of the order of operations?

Here are five related questions to consider:

  1. What are the rules for evaluating negative exponents?
  2. How does changing the signs inside parentheses affect exponents?
  3. Can you explain why multiplication comes after exponents in PEMDAS?
  4. What happens if parentheses are omitted in an expression like this?
  5. How does cubing a negative number affect its sign?

Tip: Always double-check parentheses and exponents when simplifying complex expressions.

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Exponents
Negative Numbers
Multiplication
Subtraction

Formulas

PEMDAS/BODMAS
(a - b)^n = a^n - b^n for specific values of a, b, and n

Theorems

Exponent Rules
Order of Operations (PEMDAS/BODMAS)

Suitable Grade Level

Grades 6-8

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