Algebra 2: Properties of Exponents

Questions and Answers

What is the product property of exponents?

a^m * a^n = a^(m+n)

What is the quotient property of exponents?

a^m / a^n = a^(m-n)

What is the definition of negative exponents?

a^-n = 1/a^n or (a/b)^-n = (b/a)^n

What is the value of a raised to the zero exponent?

1 Signup and view all the answers

What is the power of a power property?

(a^m)^n = a^(mn) Signup and view all the answers

What is the power of a product property?

(ab)^m = a^m * b^m Signup and view all the answers

What is the power property of equality?

If a = b, then a^n = b^n Signup and view all the answers

What is the common base property of equality?

If a^n = a^m and a is not equal to 1, then n = m Signup and view all the answers

What is the power of a quotient property?

(a/b)^n = a^n / b^n Signup and view all the answers

Study Notes

Properties of Exponents

Product Property of Exponents: States that when multiplying two exponential terms with the same base, the exponents are added: ( a^m * a^n = a^{m+n} ).
Quotient Property of Exponents: Describes the operation of division for exponential terms with the same base, where the exponents are subtracted: ( \frac{a^m}{a^n} = a^{m-n} ).
Definition of Negative Exponents: Indicates how to express negative exponents; a negative exponent represents the reciprocal: ( a^{-n} = \frac{1}{a^n} ) and ( \left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^{n} ).
Zero Exponents: States that any base raised to the power of zero equals one: ( a^0 = 1 ).
Power of a Power Property: Relates to raising an exponent to another power, which results in multiplying the exponents: ( (a^m)^n = a^{mn} ).
Power of a Product Property: Describes the distribution of an exponent over a product of bases: ( (ab)^m = a^m b^m ).
Power Property of Equality: States that if two values are equal, their powers are also equal: If ( a = b ), then ( a^n = b^n ).
Common Base Property of Equality: Indicates that if two exponential expressions with the same base are equal, then their exponents must also be equal: If ( a^n = a^m ) and ( a \neq 1 ), then ( n = m ).
Power of a Quotient Property: Outlines how to apply an exponent to a fraction, distributing the exponent to both the numerator and denominator: ( \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} ).

Description

This quiz covers the essential properties of exponents found in Algebra 2, specifically Section 5.2. Explore key concepts such as the product and quotient properties, negative exponents, and the definition of zero exponents through flashcards for effective learning.