Bridget Kearney Mod Algebra II Mod. 3

Multiplication of Exponents (powers with same bases) When the bases are the same, you find the new power by adding the exponents. Example: (x^5)(x^6) X^5 = (x)(x)(x)(x)(x) and x^6 = (x)(x)(x)(x)(x)(x) (x^5)(x^6) = (x)(x)(x)(x)(x)(x)(x)(x)(x)(x)(x) = x^11

Multiplication of Exponents (powers with different bases) Powers with different bases and unequal exponents can not be combined. Example: (x³ )(y^4 ) = (x)(x)(x)(y)(y)(y)(y) If the bases are different but the exponents are the same, then you may combine them. Example: (x³)(y³) = (x)(x)(x)(y)(y)(y) x)(x)(x)(y)(y)(y) = (x)(y)(x)(y)(x)(y) = (xy)(xy)(xy) =(xy)³

Division of Exponents (with like bases) For division with like bases you subtract exponents. Example: X^8÷x^5 =x^(8-5) =x³

Division of Exponents (with different bases) Division of unlike bases can only be combined if the exponents are equal. Example: x³÷y³ = xxx/yyy = (x/y)(x/y)(x/y) = (x/y)³

Division of Exponents (with negative exponents in the denominator) A negative exponent moves the power to the opposite side of the fraction bar. Example:

1. a^7 ÷ b^ ² × 4³ 3. 8³ x³ 4. 5^4 × 5^6 5. p^11 ÷ p^6 6. r^(-11) ÷ r^(-2)

1.(a/b) ^7 2. cannot be simplified. 3. (8x)³ 4. 5^10 5. p^5 6. 1/r^9