1. WORDS
ZERO PRODUCT PROPERTY: A base raised to the power of 0 is equal to 1
NEGATIVE EXPONENT PROPERTY: A negative exponent of a number is equal to the reciprocal of the positive exponent of the number
PRODUCT OF POWERS PROPERTY: When multiplying terms (with the same base) containing exponents, ADD the exponents
QUOTIENT POWER PROPERTY: When dividing terms (with the same base) containing exponents, SUBTRACT the exponents
POWER OF A POWER PROOPERTY: When a term with an exponent is being raised to a power
POWER OF A PRODUCT PROPERTY: To find the power of a product, distribute the exponent
POWER OF A QUOTIENT PROPERTY: To find the power of a quotient, distribute the exponent
SYMBOLS
𝑎 0 =1
𝑎 −𝑚 = 1 𝑎 𝑚
𝑎 −𝑚 𝑛 = 1 𝑎 𝑚 𝑛 𝑤ℎ𝑒𝑟𝑒 𝑎≠0, 𝑛≠0
𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛
𝑎 𝑚 𝑎 𝑛 = 𝑎 𝑚−𝑛
𝑎 𝑚 𝑛 = 𝑎 𝑚∙𝑛
𝑎𝑏 𝑚 = 𝑎 𝑚 𝑏 𝑚
𝑎 𝑏 𝑚 = 𝑎 𝑚 𝑏 𝑚
NUMBERS
8 0 =1
3 −2 = = 1 9
4 −2 3 =
𝑥 3 ∙ 𝑥 4 = 𝑥 7
2 3 ∙ = 2 5 =32
𝑥 6 𝑥 4 = 𝑥 2
= 3 3 =27
𝑥 = 𝑥 12
2𝑥 3 = 𝑥 3 = 8𝑥 3
2 𝑥 3 = 𝑥 3 = 8 𝑥 3

2. Exponents to Radicals
𝒙 𝟏 𝟐
𝟓 𝟏 𝟑
𝒚 𝟑 𝟐
𝟖 𝟑 𝟓 𝒙
𝟑 𝟓
𝒚 𝟑
𝟓 𝟖 𝟑

3. Radicals to Exponents 𝒙 𝟑 𝒚 𝟒 𝟓 𝟒 𝟑 𝒙 𝟐 𝒙 𝟏 𝟐 𝒚 𝟒 𝟑 𝟒 𝟑 𝟓 𝒙 𝟐 𝟐
𝟑 𝒚 𝟒
𝟓 𝟒 𝟑
𝒙 𝟐
𝒙 𝟏 𝟐
𝒚 𝟒 𝟑
𝟒 𝟑 𝟓
𝒙 𝟐 𝟐
= 𝒙 𝟏 =𝒙