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Step 1:I'll solve this problem step by step, focusing on explaining expressed and implied powers clearly:
Step 2:: Understanding Expressed Powers
2^{3} = 2 \times 2 \times 2 = 8
Expressed powers are exponents that are explicitly written out in a number's notation. In an expressed power, the exponent is directly shown. Example of an Expressed Power: Here, the power of 3 is directly written as an exponent, making it an expressed power.
Step 3:: Understanding Implied Powers
2 \times 2 \times 2 = 8
Implied powers are exponents that are not directly written but are understood from the context or mathematical convention. Example of an Implied Power: In this case, the power of 3 is implied by the repeated multiplication, even though no explicit exponent is shown.
Step 4:: Key Differences
- Expressed powers have the exponent visibly written - Implied powers require understanding the repeated multiplication without showing the exponent
Final Answer
- Expressed Power: 2^{3} (exponent is explicitly written) - Implied Power: 2 \times 2 \times 2 (exponent is understood but not written) Both represent the same mathematical operation of multiplying 2 three times to get 8.
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