Properties_of_Exponents - Product & Power Rules - 2

A set of flashcards defining the vocabulary and rules for simplifying algebraic expressions with exponents based on the Kuta Software Infinite Algebra 1 worksheet.

Product Rule of Exponents

To multiply powers with the same base, you add the exponents, as seen in the expression $2m^2 \cdot 2m^3 = 4m^5$.

Quotient Rule of Exponents

To divide powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator, as seen in the expression $\frac{3n^4}{3n^3} = n$.

Power of a Power Rule

To simplify a power raised to another power, you multiply the exponents, as seen in the expression $(a^m)^n = a^{m \cdot n}$ (e.g., $(4a^3)^2 = 16a^6$).

Power of a Product Rule

To find the power of a product, apply the external exponent to every factor inside the parentheses, as seen in the expression $(4xy)^{-1} = \frac{1}{4xy}$.

Zero Exponent Property

Any nonzero number or variable raised to the power of zero is equal to $1$, as seen in the expression $(x^2)^0 = 1$.

Negative Exponent Property

A base raised to a negative exponent is equivalent to its reciprocal with a positive exponent: $a^{-n} = \frac{1}{a^n}$. Expressions like $4r^{-3}$ are simplified by moving the base to the denominator.

Simplifying Algebraic Fractions

The process of using exponent rules to ensure each base appears only once and all exponents are positive, as required by the worksheet instructions.

Base

The number or variable that is being raised to a power. In the expression $4n^4$, $n$ is the base.

Coefficient

The constant multiplier of a variable. In the expression $4n^4 \cdot 2n^{-3}$, $4$ and $2$ are the coefficients.