Podcast
Questions and Answers
How do you raise a fraction to an exponential power?
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?
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?
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?
What does a number become when you raise it to the power of 0?
What does the number 0 become when you raise it to the power of 0?
What does the number 0 become when you raise it to the power of 0?
What does the number 0 become when you raise it to any positive power?
What does the number 0 become when you raise it to any positive power?
How do I substitute values for variables with exponents?
How do I substitute values for variables with exponents?
What is a power?
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.
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