Algebra 1 - Exponents Flashcards

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.