Name_______________________________________ LAWS OF EXPONENTS CHART Topic with Examples Exponent Law Steps to Simplify Adding Polynomials When ADDING polynomials 1.) Add coefficients with like 2
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(2a + 4b) + (5a + b + 9c) exponents DO NOT change. variables and exponents (red) 2.) Add coefficients with like variables (blue) 3.) Anything you cannot combine bring down in your answer. (green) Subtracting Polynomials When SUBTRACTING 1.) Distribute the subtraction 2
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(3x + 8y – 5) – (2x – 7y + 12) polynomials exponents DO sign through to each term in the NOT change second set of parenthesis. (red) **Remember distributing just changes the signs** 2.) Combine like terms All x2 (blue), all y’s (green), constants (orange) Multiplying Monomials Multiply the coefficients, add 1.) Multiply the “big” numbers (4y2z)(2y4z5) the exponents (blue) 2.) Add the exponents of the like variables (y’s=green, z’s=red) Dividing Monomials Divide/simplify the 1a.) Divide the “big” numbers A.) coefficients, subtract the (blue) ! !
exponents 2a.) Subtract the like variable 18𝑥 𝑦
exponents (x’s= red) 2𝑥 !
3a.) Keep the “y” on top when there is nothing to combine with. !
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1b.) Simplify 25/15 by dividing B.) both the top and bottom by the !"! ! ! !
GCF. (blue) 2b.) Subtract like variables exponents (a’s = red) 3b.) Keep the “c” on the bottom (green) Power of a Power (Multiplication) Distribute the outside 1a.) Distribute the 2 to the 3
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2 A.) (3x y )
exponent to each term inside coefficient 3 = 32 (blue) the parenthesis 2a.) Multiply the 2 outside the parenthesis to each exponent inside the parenthesis. (red) Power of a Power (Multiplication) 1b.) Distribute the outside 3 to the first set of parenthesis. (blue) 2b.) Distribute the outside 2 to the second set of parenthesis (red) 3b.) Multiply the “big” numbers (green) 4b.) Add the like variables exponents (orange) B.) (2x)3(5x2)2 Power of a Power (Division) 2 !!! !
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Distribute the outside exponent to each term inside the parenthesis, then follow division rule. 1.) Distribute the outside exponent 2 to all the top terms (blue) 2.) Distribute the outside exponent 2 to all the bottom terms (red) 3.) Divide the “big” numbers (green) 4.) Subtract the like variables exponents (orange) Negative Exponents A.) 5a-­‐3 B.) !!
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Zero Exponents x0 You cannot have negative exponents in your final answer. 1a.) If the negative exponent is on the top it jumps to the bottom (red) 1b.) If the negative exponent is on the bottom it jumps to the top (blue) Anything to the zero power =1