- When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution. 5 1 𝑏3 ⋅ 𝑏3 5 1 = 𝑏3 + 3 =𝑏 1 1 1 = 33 + 2 5+1 3 =3 6 = 𝑏3 1 55 ⋅ 55 3 1 = 55 + 5 2+3 6 =5 𝟓 𝟔 = 𝟓𝟓 =𝟑 = b2 3 1 33 ⋅ 32 3+1 5 𝟒 - When you are dividing terms that have the same base, just subtract their exponents to find your answer. 2 3 43 1 =4 4 87 𝑎5 1 2 43 𝑎5 87 2 1 − 3 3 3 1 − 5 5 4 2 − 7 7 𝟏 = 𝟒𝟑 7 = 36 =𝑎 𝟐 = 𝒂𝟓 7 = 36 =8 𝟐 = 𝟖𝟕 7 = 36 - If a power is being raised to another power, multiply the exponents and leave the base the same. 1 1 2 (53 ) 1 1 3 2 =5( ⠂ ) 1 2 3 (23 ) = 51/6 2 1 5 (95 ) 1 2 5 5 =2( ⠂ ) =9( ⠂ ) = 22/9 = 92/25 2 1 3 3 - When any base is being multiplied by an exponent, distribute the exponent to each part of the base. 2 (𝑥𝑦)3 𝟐 𝟑 𝟐 𝟑 =𝒙 𝒚 1 (25⠂9)2 1 (27⠂8)3 1 2 1 3 = 25 ⠂9 1 2 = 27 ⠂8 = 5⠂3 = 3⠂2 = 𝟏𝟓 =𝟔 1 3 - The power of a quotient is equal to the quotient obtained when the numerator and denominator are each raised to the indicated power separately, before the division is performed. = 2 83 2 273 1 2 2 8 3 ( ) 27 = = (23 )3 2 (33 )3 4 2 ( ) 16 27 3 ( ) 8 4 = 1 = 𝟒 = 1 1 2 𝟗 = 42 = 1 162 (33 )3 1 (23 )3 1 𝟏 = 𝟐 1 (22 )2 273 1 83 = 𝟑 𝟐 1 (4 2 )2 - Any base with an exponent of zero is equal to one. a0 = 1 𝑎 0 ( ) 𝑏 20 = 1 = 1 - A number with a negative exponent should be put to the denominator, and vice versa. 8 = = = 2 −3 27 1 2 1 (8 ⁄3 ) 1 = = 22 𝟏 𝟒 = 1 −3 1 1 27 ⁄3 4 = 1 31 = 𝟏 𝟑 = 3 −2 1 3 1 (4 ⁄2 ) 1 23 𝟏 𝟖 - When changing expressions from exponential form to radical form, write the radical sign, copy the base it becomes the radicand, and exponent in the numerator becomes the power of the radicand and the exponent in the denominator becomes the index. b3/5 52/3 = 𝟓 𝟑 = √𝒃𝟑 √𝟓𝟐 (x3y2)3/4 𝟒 = √(𝒙𝟑 𝒚𝟐 )𝟑 - When changing radical expression to exponential form, copy the radicand, it becomes the base now, the power becomes exponent in the numerator, and the index becomes the denominator of the rational exponent. 5 15 √𝑏 3 = 15b3/5 3 30 √𝑎2 = 30a2/3 5 √𝑎4 = a4/5