Unit 2 Exponents and Algebra
1. Exponent Laws
a) Product Rule: xmxn=xm+n
Examples: Simplify
-2ab54a4b3
=-24aa4b5b3
=-8a1+4b5+3
=-8a5b8
b) Quoent Rule: xmxn=xm-n
Examples: Simplify
x7y4x3y4=x7-3y4-4
=x4y0
=x4
c) Power of a Power Rule: xmn=xmn
Examples: Simplify
2x2y73=23x23y73
=8x23y73
=8x6y21
Some more exponent rules:
xyzm=xmymzm
xym=xmym,y0
x0=1,x0
2. Distribuve Property: ab+c=ab+ac
Examples: Simplify
-2x(3x+5)
=-2x(3x)-2x(5)
=-6×2-10x
3. Simplifying expressions (Adding and Subtracng Polynomials)
Examples: Simplify
3(x + 5)-2(x-6)
=3x + 35-2x-26 Distribute
=3x+15-2x+12 Simplify (Multiply)
=3x-2x+15+12 Collect Like Terms
=x+27 Simplify (Add/Subtract)
