Exercícios do ponto
1: Callelle an rotineia:
a) $3^3=\frac{3.3}{2}-3=27$
b) $5^4=5 \cdot 5 \cdot 5 \cdot 5=625$
25/123/625
2: Usands as Pespriedades, sim reifique. a) $8^{\prime \prime}, 8^{20}=8=820
Answer (2)
The calculations of 3 3 and 5 4 reveal that while 3 3 equals 27, the accompanying expression is incorrect. Additionally, both 8 11 and 8 20 do not equal 8 or 820, indicating that statement is inaccurate. Therefore, the first and third statements contain errors, while the second statement regarding 5 4 is correct.
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Calculate 3 3 which equals 27, but the expression 2 3 ⋅ 3 − 3 is not equal to 27.
Calculate 5 4 which equals 625, and the given expression is correct.
Calculate 8 11 and 8 20 , which are not equal to 8 or 820, so the given expression is incorrect.
The first expression contains an error, the second is correct, and the third contains an error.
Explanation
Evaluating 3 3 Let's analyze the given expressions and verify their correctness.
First, we have 3 3 . This means 3 × 3 × 3 , which equals 27. The problem states that 3 3 = 2 3 ⋅ 3 − 3 = 27 . Let's check if 2 3 ⋅ 3 − 3 is indeed equal to 27. 2 3 ⋅ 3 − 3 = 2 9 − 3 = 4.5 − 3 = 1.5 . This is not equal to 27, so the first part of the equation is incorrect. However, the final result 3 3 = 27 is correct.
Evaluating 5 4 Next, we have 5 4 . This means 5 × 5 × 5 × 5 , which equals 625. The problem states that 5 4 = 5 ⋅ 5 ⋅ 5 ⋅ 5 = 625 . This is correct.
Evaluating 8 11 and 8 20 Finally, we have 8 ′′ , 8 20 = 8 = 820 . I assume that 8 ′′ means 8 11 . So, we have 8 11 , 8 20 = 8 = 820 . Let's evaluate 8 11 and 8 20 .
8 11 = 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 = 8589934592 8 20 = 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 = 1152921504606846976 The statement 8 11 , 8 20 = 8 = 820 is incorrect.
Examples
Understanding exponents is crucial in many fields, such as computer science (where data sizes are often expressed as powers of 2), finance (where compound interest involves exponential growth), and physics (where phenomena like radioactive decay are modeled using exponential functions). By mastering exponents, you can analyze and predict outcomes in these diverse areas, making informed decisions and solving complex problems.
