MATH Basic Algebra II  - Unit 4: Operations with Numbers and Exponents
Order of Operations

In the following problems, use the Order of Operations to evaluate.

1) Evaluate. 
 
Remember:  Multiplication takes priority over addition by the Order of Operations.

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2) Evaluate. 

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3) Evaluate. 
 
Hint:  Evaluate inside brackets first, then multiply by 9.

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4) Evaluate.
 
Hint: Remember to start with the inside parentheses. 
 
Be careful.  Along the way you will need to multiply before subtracting, all based on the rules for Order of Operations.

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Properties of Exponents

5) Evaluate. 
 
Hint:  The negative exponent means to write the reciprocal of the base to the same power as a positive.

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6) Evaluate. 
 
Hint:  Any number or expression to the zero power is equal to?

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7) Evaluate.
 
Hint:  Apply the Power of a Quotient Property.

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In the following problems, simplify each expression.  Assume no variable equals zero and express the answers with positive exponents.

8) Simplify. 

9) Simplify. 

10) Simplify each expression.  Assume no variable equals zero.

11) Simplify each expression.  Assume no variable equals zero.

12) Simplify.

Rational Exponents

13) Evaluate.

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14) Evaluate.

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15) Write the radical expression in exponential form.

16) Write the radical expression in exponential form.

17) Write the exponential expression in radical form.

18) Write the exponential expression in radical form.

19) Simplify.

20) Simplify.

21) Simplify.       

22) Simplify.

23) Simplify. 

24) Simplify.

Review

25) Identify the slope (m) and y-intercept (b) of the equation: –0.6x + y = –4.
 
Hint:  Put the equation in slope-interceptform first.   y = mx + b
 
Click here to review the unit content explanation for Linear Equations.

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26) Write an equation of the line that contains the point (5, –2) and is perpendicular to 2x – 5y = 15. Express the equation in slope-intercept form.
 
Hint:  Put the equation in slope-intercept form first and remember that the slopes of perpendicular lines are OPPOSITE reciprocals.
 
Click here to review the unit content explanation for Linear Equations.

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27) Solve for m.   
 
Hint:  Use cross products first and that will eliminate the fractions in the equation.
 
Click here to review the unit content explanation for Solving Equations and Applications.

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28) Solve x:  7x – 22 = 3x + 18
 
Click here to review the unit content explanation for Solving Equations and Applications.

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29) Solve the inequality:  5z – 6 > 14
 
Click here to review the unit content explanation for Inequalities and Absolute Value Equations.

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