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Simplifying Expressions
| Rule |
Example |
Description |
| Product |
56 x 53 = 59 |
na x nb = na+b |
| Quotient |
56 / 53 = 53 |
na / nb = na-b where n ≠ 0 |
| Power of a power |
(52)3 = 56 |
(na)b = naxb |
| Power of a product |
(3x4)5 = 35x45 |
(nm)a = nama |
| Power of a quotient |
(3/4)2 = 32/42 |
(n/m)a = na/ma |
| Zero as an exponent |
50 = 1 |
n0 = 1 |
| Negative exponents |
5-2 = 1/52 |
n-a = 1/na |
| Rational exponents |
82/3 =
3√82 |
na/b =
b√na =
(b√n)a |
| Distributive property |
4(x+1) = 4x+4 |
a(b+c) = ab + ac |
| Common factor |
4x+4 = 4(x+1) |
ab + ac= a(b+c) |
| Product of Binomials |
(x-1)(x+2) = x2+x-2 |
(a+b)(c+d) = ac+ad+bc+bd |
| Factoring Trinomials |
x2+x-2 = (x-1)(x+2) |
ax2+bx+c = (mx+n)(jx+k) |
| Eliminating fractions |
x/2=y/3 => 3x=2y |
a/b=m/n => an=mb |
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