The Powers of Numbers
A little exponent goes a long way!
You are correct. In a multiplication that involves more than two factors, the order in which the multiplications are done makes no difference in the product.
2 × 3 × 5 = 5 × 3 × 2 = 2 × 5 × 3 = 3 × 2 × 5 = 30
Now, in the multiplications we have just discussed, the factors in any one multiplication have all been different numbers. In the multiplication
3 × 4 = 12
for example, we used 3 as a factor once, and 4 as a factor once. In the multiplication
2 × 3 × 5 = 30
we used 2 as a factor once, 3 once, and 5 once.
But we can have multiplications in which we use the same number (same quantity, that is) as a factor more than once, can’t we? For example, in
2 × 2 = 4
we use 2 as a factor twice.
What product do we get if we use the number 3 as a factor twice?
Answer to Self-Test Question 4, Lesson 1 :
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