Sure! Let's go through each section step by step.
Function of the Day
To arrange a, b, c, d, e, f, and g from least to greatest, you'll first need the numerical values of each variable. Since those aren't provided here, let’s assume you have those values from your previous work or given equations.
Example Values:
- a = 3
- b = -2
- c = 5
- d = 0
- e = -1
- f = 4
- g = -3
Steps to Arrange:
- List the values: 3, -2, 5, 0, -1, 4, -3
- Determine the least value: -3 (g)
- Next least: -2 (b), followed by -1 (e), 0 (d), 3 (a), 4 (f), 5 (c).
- Arrange in order: -3, -2, -1, 0, 3, 4, 5
Arranged Order: g, b, e, d, a, f, c
Vocabulary Terms
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Exponent: A number that shows how many times to multiply the base by itself. For example, in \(3^2\), 2 is the exponent.
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Base: The number that is multiplied by itself. In \(3^2\), the base is 3.
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Standard form vs. Exponent form:
- Standard form represents numbers in their usual numeric notation (e.g., 9).
- Exponent form represents numbers using exponents (e.g., \(3^2\) for 9).
5 Problems
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What does \(x^4\) mean?
- It means \(x \times x \times x \times x\).
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What operation are you doing?
- You are performing multiplication repeatedly.
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What does \(3^{-4}\) mean?
- It means \(\frac{1}{3^4}\) or the reciprocal of \(3^4\).
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Is your answer negative?
- No, the answer is positive since it's the reciprocal of a positive number.
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What is \(-25\) and how does it compare to \((-2)^5\)?
- \(-25\) is simply negative twenty-five.
- \((-2)^5 = -32\).
- They are different in value because \(-25\) does not involve exponentiation of a base negative number.
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Why are they different?
- Because the exponentiation changes the base's sign when raised to an odd power and scales the result by the number of multiplications.
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What is (-(-3)^3?
- First, evaluate \((-3)^3 = -27\).
- Thus, \(-(-3)^3 = -(-27) = 27\).
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What do you think of when you hear the word “exponents”? What operation?
- I think of repeated multiplication.
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How is it different?
- It’s different from regular multiplication because it deals with how many times a number is multiplied by itself rather than how many separate numbers are multiplied together.
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Example: What is the difference between \(3(2)\) and \(3^2\)?
- \(3(2) = 6\), which is multiplication of 3 and 2.
- \(3^2 = 9\), which is \(3 \times 3\).
What do I need help with?
If there’s a specific problem or concept you’re struggling with, let’s break that down or practice it further! Feel free to ask questions or clarify what you need help with.
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