Properties_of_Exponents - Polynomials - 3

This set of vocabulary flashcards covers the fundamental properties of exponents used to simplify algebraic expressions as presented in the Infinite Algebra 1 worksheet.

Product Rule of Exponents

A property used to simplify expressions like $2m^2 imes 2m^3$ stating that when multiplying powers with the same base, you add the exponents: $a^m imes a^n = a^{m+n}$.

Power of a Power Rule

A property used to simplify expressions like $(x^2)^0$ or $(3k^4)^4$ stating that to find a power of a power, you multiply the exponents: $(a^m)^n = a^{m imes n}$.

Power of a Product Rule

A property used to simplify expressions like $(2x^2)^{-4}$ or $(4xy)^{-1}$ stating that the power of a product is the product of the powers: $(ab)^n = a^n b^n$.

Zero Exponent Rule

A property stating that any non-zero base raised to the power of zero is equal to $1$, as seen in the expression $(x^2)^0$.

Negative Exponent Rule

A property stating that a base raised to a negative exponent is equal to its reciprocal with a positive exponent: $a^{-n} = \frac{1}{a^n}$.

Quotient Rule of Exponents

A property used to simplify expressions like $\frac{r^2}{2r^3}$ or $\frac{3n^4}{3n^3}$ stating that when dividing powers with the same base, you subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.

Positive Exponent Requirement

A formatting rule in the worksheet specifying that the final simplified answer should only contain positive exponents.

Coefficient Multiplication

The process of multiplying the numerical factors in front of variables, such as multiplying $4 imes 2$ in the expression $4n^4 imes 2n^{-3}$.