Questions and Answers
What is 0.00001 as a power of 10?
1 * 10^-5
Evaluate: 8^-2
1/64
Simplify: (2x^5/8x)^-3
64/x^12
Simplify: b^3m-7 b^4m+12/ b^3
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Write 4.8 in scientific notation.
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Write 0.000002 in scientific notation.
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Write 0.0042 in scientific notation.
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What is the numerator of an exponent?
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Write 5,400,000 in scientific notation.
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If b^n = b^m, what can we conclude?
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What is the negative exponent law?
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What is 10^4?
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What is 10^-4?
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What does power to power mean?
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What is the negative quotient power property?
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What is the order of operations for complex exponent problems?
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What is the denominator of an exponent?
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Prove that: root b = b^k.
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Solve 64^(5/3).
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When solving big radical exponent variable problems, what should you remember?
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What should you remember when writing something in scientific notation?
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What is the importance of distributing?
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What should you do with big fraction exponent problems?
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What should you remember when multiplying polynomials?
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How do you find the degree of a polynomial?
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What should you do when subtracting polynomials?
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What should you write about exponent problems?
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What are roots?
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What is scientific notation?
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What are polynomials?
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Study Notes
Powers of Ten and Scientific Notation
- 0.00001 expressed as a power of 10 is 1 * 10^-5.
- 4.8 in scientific notation is 4.8 * 10^1.
- 0.000002 is represented as 2 * 10^-6.
- 0.0042 can be written in scientific notation as 4.2 * 10^-3.
- 5,400,000 is represented as 5.4 * 10^6.
Exponents and Their Properties
- Evaluating 8^-2 results in 1/64.
- Simplifying (2x^5/8x)^-3 gives 64/x^12.
- For b^n = b^m, it holds that n = m.
- Negative exponent law states that a base with a negative exponent translates to the reciprocal of the base raised to the positive exponent.
- Power to power property: (x^a)^b equals x^(ab).
Simplifying Expressions
- Simplifying the expression b^3m-7 b^4m+12 divided by b^3 results in b^(7m + 2).
- When solving big radical exponent variable problems, remember the cubed root of a number is equivalent to raising that number to the 1/3 power.
- When subtracting polynomials, add the opposite to simplify the expression.
Order of Operations for Exponents
- The order of operations for complex exponent problems is:
- Apply negative quotient power property,
- Use power to power rule,
- Multiply powers with the same base,
- Divide powers with the same base,
- Use zero or negative exponent rules.
Additional Concepts
- The numerator of an exponent is referred to as the "inside".
- The denominator of an exponent represents the "outside".
- k equals 1/2 when proving that root b is equal to b^k.
- In polynomial problems, find the degree by adding all the exponents and remember to simplify by dividing numbers where possible.
Operations with Polynomials
- When multiplying polynomials, utilize a chart to organize the calculations.
- Always start with distribution when managing expressions.
General Rules for Scientific Notation
- When writing in scientific notation, ensure the coefficient (the number) is between 1 and 9.
Studying That Suits You
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Description
Prepare for your Algebra 1 Unit 8 test with these flashcards covering key concepts such as powers of ten, scientific notation, and simplification of expressions. Each card presents a question alongside its answer, facilitating effective review and memorization.
