Questions and Answers
How do you raise a fraction to an exponential power?
The numerator and denominator need to be raised in the same way.
What does it mean when a number is squared?
That number is raised to the power of 2.
What does it mean when a number is cubed?
That number is raised to the power of 3.
What does a number become when you raise it to the power of 0?
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What does the number 0 become when you raise it to the power of 0?
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What does the number 0 become when you raise it to any positive power?
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How do I substitute values for variables with exponents?
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What is a power?
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Study Notes
Exponents and Fractions
- To raise a fraction to an exponential power, both the numerator and denominator must be raised to the same exponent, e.g., ((\frac{2}{3})^3 = \frac{2^3}{3^3} = \frac{8}{27}).
Squaring Numbers
- Squaring a number means raising it to the power of 2, which is represented mathematically as (x^2).
Cubing Numbers
- Cubing a number involves raising it to the power of 3, indicated as (x^3).
Any Number Raised to Power of Zero
- Raising any number (except zero) to the power of 0 results in 1; formally, (x^0 = 1).
Zero Raised to Power of Zero
- Raising zero to the exponent of 0 is considered undefined, meaning it does not generate a valid number.
Zero Raised to Positive Powers
- When zero is raised to any positive exponent, it remains zero, expressed as (0^n = 0) for (n > 0).
Substituting Values with Exponents
- When substituting variable values in expressions with exponents, it is crucial to use parentheses to ensure accurate simplification and maintain the order of operations.
Understanding Powers
- A power signifies how many times a number (the base) is used as a factor in multiplication, e.g., (x^n) means (x) is multiplied by itself (n) times.
Studying That Suits You
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Description
Test your understanding of exponents with these flashcards designed for Algebra 1. Each card provides essential definitions and examples to help you grasp the concepts of raising numbers and fractions to powers. Perfect for quick revision and mastering exponents.
