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# GMAT - Algebra

### Key GMAT Algebra

-1^2= 1
0^2= 0
1^2= 1
2^2= 4
2^3= 8
2^4= 16
2^5= 32
2^6= 64
3^2= 9
3^3= 27
3^4= 81
4^2= 16
4^3= 64
4^4= 256
5^2= 25
6^2= 36
5^3= 125
5^4= 625
7^2= 49
8^2= 64
9^2= 81
10^2= 100
11^2= 121
12^2= 144
13^2= 169
14^2= 196
15^2= 225
20^2= 400
25^2= 625
x^0= 1 if x not equal to 0
x^1= x
What are the "Order of Operations"? 1. () -> inner most first 2. ^ 3. x 4. / 5. + 6. -
(x^5)(x^-4) = x
(2/7)(5/3) = 10/21
(x^a/x^b)= x^(a-b)
x^-a= 1/x^a
(x^a)^b= x^ab
x^a + x^b = x^(a+b)
(2/7) / (3/5) = 10/21
1/(y^-b) = y^b
(5xyz^2)^2 = 25(x^2)(y^2)(z^4)
x^(1/2) = sqrt(x)
sqrt(2) = 2^(1/2)
sqrt(1) = 1
sqrt(x^2) = |x|
sqrt(2^4) = 2^(4/2) = 4
sqrt(72) = 6sqrt(2)
sqrt(3) x sqrt(12) = sqrt(36) = 6
sqrt(2) + sqrt(2) + sqrt(2) = 3sqrt(2)
sqrt(16) 4
Solve for x x^2 = 16 4 or -4
What is the coefficient of 3y^2 3
Solve for x x^2 + 8x + 16 = 0 -4
Solve for x x^2 – 18x +81 = 0 9
Solve for x x^2 – 64 = 0 -8 or 8
Solve for x (x+8)(x-8)=0 -8 or 8
(x-9)^2 = 0 9
(x+4)^2 = 0 -4
Percent Difference 5 increased to 8 60%
6,000,000 / 12,000 = 500
Solve for y: 3y-3 < 5y+7 y > -5
Solve for x: |2x-3| = 7 5 or -5
Solve for x: 2 < x+2 < 4 0 < x < 2
Solve for y: -2y < 10 y > -5
Created by: 29705394