Problem 80 - College Algebra Essentials

Question

State the name of the property illustrated. $$7 \cdot(11 \cdot 8)=(11 \cdot 8) \cdot 7$$

Step-by-Step Solution

Answer

The property illustrated is the associative property of multiplication.

Step 1: Identify the property

The expression demonstrates a property where the grouping of factors doesn't change the product. This is known as the associative property of multiplication. It is formally defined as: for any real numbers a, b, and c, the equation \(a \cdot (b \cdot c) = (a \cdot b) \cdot c\) holds.

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Step 6: Conclude with the answer

The property illustrated is the associative property of multiplication.