Question

Dividing Powers with the Same Base
The table represents the metric volume measure of a liter. Each amount is represented by its power of 10.

A 2-column table with 5 rows. Column 1 is labeled Unit with entries centiliter, liter, hectoliter, kiloliter, megaliter. Column 2 is labeled Power of 10 with entries 10 Superscript negative 2, 10 Superscript 0, 10 squared, 10 cubed, 10 Superscript 6.

Complete the work to determine how many times larger a megaliter is than a hectoliter.

1. Divide powers:
106
102
2. Expand each power:
10 • 10 • 10 • 10 • 10 • 10
10 • 10
3. Divide common factors:
10 • 10 • 10 • 10 • 10 • 10
10 • 10
4. Simplify.
A megaliter is
times larger than a hectoliter.

Answer 1

1. Divide powers: 10^6 / 10^2 = 10^(6−2)
2. Expand each power: (10·10·10·10·10·10) / (10·10)
3. Divide common factors: cancel two 10s from numerator and denominator → 10·10·10·10
4. Simplify: 10·10·10·10 = 10^4 = 10,000

A megaliter is 10,000 times larger than a hectoliter.