# SAT Lesson 12

SAT MATH Lesson 12
Drill Day 12
Simplify the following expressions:
1.
(3x3 yz2 )(5xy2 )
4. (4xy2 )3
1
2 2
7. (4 x )
2.
5.
8.
42a 3
2
7a
 5a 
 
 2b 
6
2
2
3.
8a 2bc3
2 4
24a b c
6.
16 y 2
9.  2 
3
3
Algebraic Expressions
Algebraic Expressions contain numbers, variables, and the symbols for
operations. Since algebraic expressions themselves represent numbers
they can be added, subtracted, divided and multiplied. Some examples
of algebraic expressions are:
b
a b
3
x  7, 3x  1, y  ab, , 6(2 x  y ),
r
c
2
Like terms are terms that contain the same variables with corresponding
variables having the same exponents.
Simplify: 3x 2  2 x  2 x 2  5 x  4
The distributive property allows you to distribute multiplication over
8(4x + 7) = 8(4x) + 8(7) = 32x + 56
To evaluate and algebraic expression, substitute the numeric value of the
variable in to the expression. Then evaluate the resulting numerical
expression.
Evaluate: 5  2a 3 when a = 2.
Laws of Exponents
Operation
Rule
Multiplication
Examples
(3a 2b3c)(2a 3b)  3 * 2 * a 23b33c
 6a 5b 4c
Division
Subtract the exponents
Power to a Power
Multiply the exponents
4 x5 y 3
x4
 5
8
12xy
3y
(2a 2 )3  (21*3 a 2*3 )  23 a6  8a6
Laws of Exponents
Fractional Exponents
Negative Exponents
Examples