“one degree less”

Adding and Subtracting-  you must have like terms to add or subtract

Add or subtract the coefficients, the variable and exponent stay the same

2a⁴ - 7a⁴ = -5a⁴                                              3xyz - 9xyz = -6xyz    

3b² + 8x = not like terms, they can't be added

Multiplying-  if the bases are the same, add the exponents

(x⁴)(x⁵) = x⁹                           (a⁷)(a)(a²) = a¹⁰

If no exponent is written, the exponent is 1.

Dividing- if the bases are the same, subtract the exponents

y³/y = y²             x⁵/x⁴= x

Power of a power-  multiply the exponents

(x⁷)³= x²¹  

Power of a monomial-  distribute the exponent to each of the factors (including the coefficient)

(-3a⁴)³= -27a¹²              (-2x⁵)² = 4x¹⁰              (-ab²c⁴)⁵ = -a⁵b¹⁰c²⁰ 

Power of a polynomial-  write it out in expanded form (no exponent) and use FOIL, or write it out and distribute each term to each of the other terms

(x+y)²

(x+y)(x+y)

x²+xy+xy+y²

x²+2xy+y²

Anything (except zero) to the zero power= 1          (-5)⁰ = 1     x⁰ = 1

Zero to the zero power= does not exist, undefined          0⁰ = undefined

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