15. Use the associative and commutative properties to make the calculation easier, Justify the steps. \[ 6 *(14 * 5) \]

To simplify the expression \[ 6 \times (14 \times 5) \] using the associative and commutative properties, we can rearrange the terms to make the calculation easier. 1. **Associative Property of Multiplication**: The associative property of multiplication states that the grouping of terms does not affect the product. This means we can change the grouping of terms without changing the result. 2. **Commutative Property of Multiplication**: The commutative property of multiplication states that the order of terms does not affect the product. This means we can change the order of terms without changing the result. Given expression: \[ 6 \times (14 \times 5) \] 1. Apply the associative property by changing the grouping of terms: \[ 6 \times (14 \times 5) = (6 \times 14) \times 5 \] 2. Apply the commutative property by changing the order of terms: \[ (6 \times 14) \times 5 = 14 \times (6 \times 5) \] 3. Calculate the result: \[ 14 \times (6 \times 5) = 14 \times 30 = 420 \] Therefore, the simplified result of \[ 6 \times (14 \times 5) \] is 420.