Two powers of one number, multiplied
A box holds 2³ sweets. A carton holds 2⁴ boxes. How many sweets in a carton?
Join the two rows of tiles. Count them. Then write one power.
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2³ × 2⁴ — two powers of 2. Step 1 of 4
2³ × 2⁴— two powers of 2.- Opened out:
(2×2×2) × (2×2×2×2). - Join the rows into one line: seven 2s.
2⁷= 128.
The rule
A carton holds 128 sweets, which is 2⁷.
Two powers of one base multiply by joining their factors. 2³ has three 2s and 2⁴ has four 2s. That makes seven 2s. The counts add. The base stays. 2³ × 2⁴ is 2⁷: 128 sweets.
7³ × 7⁴=7⁷. Three 7s and four 7s make seven 7s.q⁵ × q²=q⁷. Hereqstands for any number, and 5 + 2 = 7.10² × 10³=10⁵. Here 2 + 3 = 5.
The counts add only when the base is the same. 2³ × 3⁴ has two different bases, 2 and 3.