Let's address each question one by one:
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What is 4.01 x 10 to the 1st power in expanded form?
- The correct answer is 40.1. (4.01 multiplied by 10 equals 40.1).
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Simplify the expression (no expression provided).
- Please provide the expression for simplification.
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Which choices below are equivalent to 125?
- The following expressions are equivalent to 125:
- \( 5^3 \)
- \( 25 \times 5 \)
- Note: More context is needed on what specific options are available for selection.
- The following expressions are equivalent to 125:
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Simplify the expression (no expression provided).
- Please provide the expression for simplification.
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Simplify using a single exponent (no expression provided).
- Please provide the expression for simplification.
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Explain what scientific notation is and how it is used. Then, give an example of a number and its scientific notation form.
- Scientific notation is a way to express very large or very small numbers in a compact form. It is written as a product of a number (between 1 and 10) and a power of 10. For example, the number 3000 can be written in scientific notation as \( 3.0 \times 10^3 \).
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Simplify the expression to a single exponent (no expression provided).
- Please provide the expression for simplification.
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Simplify the expression (no expression provided).
- Please provide the expression for simplification.
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Give an example of the Zeroth Power Property.
- The Zeroth Power Property states that any non-zero number raised to the power of zero equals one. For example, \( 5^0 = 1 \).
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In the expression, match each item with the vocabulary word that describes it.
- Without the expression given, I cannot match the items. However, as an example:
- For the expression \( 4^3 \):
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- 4 - base
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- 3 - exponent
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- \( 4^3 \) - power
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- For the expression \( 4^3 \):
- Complete the expression below. Express your answer in scientific notation: (no expression provided).
- Please provide the expression for assistance.
- True or False (no statement provided).
- Please provide the statement to evaluate.
- Simplify the expression. Write your answer with a single exponent. (no expression provided).
- Please provide the expression for simplification.
- Simplify completely (no expression provided).
- Please provide the expression for simplification.
- Which of the following shows (no expressions provided).
- Please provide options for evaluation.
- Write the exponent below in the expanded form: (no exponent provided).
- Please provide the exponent you want to expand.
- Write 0.000058 in scientific notation.
- In scientific notation, \( 0.000058 \) can be written as \( 5.8 \times 10^{-5} \).
- Extra Credit: Explain why the Quotient Rule for exponents works.
- The Quotient Rule states that when you divide two powers with the same base, you subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \). This works because you can think of division as removing factors. For example, \( a^m \) means you have \( m \) copies of \( a \), and when you divide by \( a^n \) (which means removing \( n \) copies of \( a \)), you're left with \( a^{m-n} \), where you have subtracted the number of \( a \)s in the denominator from the numerator.
If you provide additional information or expressions for those that are incomplete, I can assist further.
0 answers