Algebra 2 Laws of Exponents Flashcards

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} )