Math Practice Problems - Simplifying Algebraic Expressions 2

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.

Problem

Correct Answer

Your Answer

( ^-4e )( 9e^-4 )

Solution

( ^-4e )( 9e^-4 )	=	-4 • e¹ • 9 • e^-4
	=	( -4 • 9 )( e¹ • e^-4 )
	=	-36 • e^{1 + -4}
	=	^-36e^-3

Problem

Correct Answer

Your Answer

( 6b^-4 )( ^-2b⁴ )

Solution

( 6b^-4 )( ^-2b⁴ )	=	6 • b^-4 • -2 • b⁴
	=	( 6 • -2 )( b^-4 • b⁴ )
	=	-12 • b^{-4 + 4}
	=	^-12

b^{-4 + 4} = b⁰ = 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.

#	Problem	Correct Answer	Your Answer
1	( 6x^-4)¹	=
Solution Any number to the 1st power is itself.

Problem

Correct Answer

Your Answer

( 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.

Correct Answer

Your Answer

9e⁴

Correct Answer

Your Answer

j⁸

Complexity=5

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

Correct Answer

Your Answer

36k⁸

Problem

Correct Answer

Your Answer

( -y⁴ )( 4y^-5 )

Solution

( -y⁴ )( 4y^-5 )	=	-1 • y⁴ • 4 • y^-5
	=	( -1 • 4 )( y⁴ • y^-5 )
	=	-4 • y^{4 + -5}
	=	^-4y^-1

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