## Simplifying Algebraic Expressions 2 - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=5, Mode=multiply

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
 1.   ( - 4e )( 9e -4 ) = 2.   ( 6b -4 )( - 2b 4 ) =

### Complexity=5, Mode=exponent

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
 1.   ( 6x -4) 1 = 2.   ( 3z -1) 4 =

### Complexity=5, Mode=root

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
1.
 9e 4
=
2.
 j 8
=

### Complexity=5

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
1.
 36k 8
=
2.   ( -y 4 )( 4y -5 ) =

### Complexity=5, Mode=multiply

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
1( - 4e )( 9e -4 ) =
Solution
 ( - 4e )( 9e -4 ) = -4 • e 1 • 9 • e -4 = ( -4 • 9 )( e 1 • e -4 ) = -36 • e1 + -4 = - 36e -3
2( 6b -4 )( - 2b 4 ) =
Solution
 ( 6b -4 )( - 2b 4 ) = 6 • b -4 • -2 • b 4 = ( 6 • -2 )( b -4 • b 4 ) = -12 • b-4 + 4 = - 12
b-4 + 4 = b 0 = 1

### Complexity=5, Mode=exponent

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
1( 6x -4) 1 =
Solution
Any number to the 1st power is itself.
2( 3z -1) 4 =
Solution
 ( 3z -1) 4 = ( 3 • z -1 )4 = ( 3 )4 • (z -1)4 = 81 • (z -1 * 4) = 81z -4

### Complexity=5, Mode=root

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
1
 9e 4
=
2
 j 8
=

### Complexity=5

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.