Algebra II Recipe: Properties of Exponents

The Properties

1. Multiplying like bases.
• Add the exponents.
• aⁿ . a^m = a^n+m
2. Power of a power.
• Multiply the exponents.
• (aⁿ)^m = a^nm
3. Power of a product.
• Raise each part of the product to the power.
• (ab)ⁿ = aⁿbⁿ
4. Negative exponent property.
• To make the negative exponent positive, move the base and its exponent to the opposite location in the fraction.
• a^-m = 1/m and 1/(a^-n) = aⁿ
5. Zero exponent property.
• Any base raised to the zero power equals one.
• aº = 1
6. Dividing like bases.
• Make any negative exponents positive.
• Find the difference of the exponents.
• The base raised to that difference goes where the larger exponent was located.
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7. Power of a quotient.
• Reduce the fraction if possible and make negative exponents positive.
• Raise each part of the numerator and denominator to the power.
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Practice Problems