As you can tell from the examples of the number lines below, not all number lines change by one unit from mark to mark. Copy the
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The product of (3.4 × 10⁻¹⁴) and (1.8 × 10²⁸) is 6.12 × 10¹⁴. Applying associative property and exponential rule, the required product is calculated.
<h3>What are the required properties?</h3>The given products are decimals and exponentials. So, the required properties are the associative and exponential rules. They are as follows:
Associative property:
a×(b × c) = (a × b)×c
From this, we can also write,
(a × b) × (c × d) = (a × c) × (b × d)
Exponential rule:
The product of two exponentials is
The given values are
3.4 × 10⁻¹⁴ and 1.8 × 10²⁸
The product of these values is
(3.4 × 10⁻¹⁴) × (1.8 × 10²⁸)
Applying the associative property: (a × b) × (c × d) = (a × c) × (b × d);
⇒ (3.4 × 10⁻¹⁴) × (1.8 × 10²⁸) = (3.4 × 1.8) × (10⁻¹⁴ × 10²⁸)
Applying exponential rule:
⇒ 6.12 × 10⁻¹⁴⁺²⁸
⇒ 6.12 × 10¹⁴
Thus, the product of the given values is 6.12 × 10¹⁴. Option A is correct.
Learn more about the exponential rules here:
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