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Algebra 2 Laws of Exponents Flashcards

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Questions and Answers

What does the Product Law of Exponents state?

Multiply the exponents when raising a power to another

Add the exponents when multiplying powers with the same base (correct)

Distribute the exponent when finding the power of a quotient

Subtract the exponents when dividing powers with the same base

What does the Power Law of Exponents involve?

Subtract the exponents when dividing powers with the same base

Add the exponents when multiplying powers with the same base

Multiply the exponents when raising one power to another (correct)

Rewrite using radicals for fractional exponents

What does the Quotient of Powers Property state?

Add the exponents when multiplying powers with the same base

Subtract the exponents when dividing powers with the same base (correct)

Multiply the exponents when raising one power to another

Distribute the exponent when finding the power of a quotient

What does the Power of a Quotient Property describe?

Distribute the exponent when finding the power of a quotient Signup and view all the answers

What are Fractional Exponents?

Exponents that can be rewritten using radicals Signup and view all the answers

What do Negative Exponents represent?

The base raised to the power of a negative is equal to one divided by the base raised to a positive exponent Signup and view all the answers

Study Notes

Product Law of Exponents

When multiplying powers with the same base, add the exponents.
Example: ( a^m \times a^n = a^{m+n} )

Power Law of Exponents

Raising a power to another involves multiplying the exponents.
Example: ( (a^m)^n = a^{m \times n} )

Quotient of Powers Property

For division of powers with the same base, subtract the exponents.
Example: ( \frac{a^m}{a^n} = a^{m-n} )

Power of a Quotient Property

To calculate the power of a quotient, distribute the exponent to both the numerator and denominator.
Example: ( \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} )

Fractional Exponents

Exponents expressed as fractions can be rewritten using radicals.
The denominator of the fraction becomes the index of the radical, while the numerator becomes the power inside the radical.
Example: ( a^{\frac{m}{n}} = \sqrt[n]{a^m} )

Negative Exponents

A base raised to a negative exponent is equivalent to one divided by the base raised to the positive exponent.
Example: ( a^{-n} = \frac{1}{a^n} )

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Description

Test your knowledge of the Laws of Exponents with these flashcards. This quiz covers essential properties such as the Product Law, Power Law, and Quotient of Powers Property. Perfect for Algebra 2 students looking to strengthen their understanding of exponent rules.