Digits, Grade 8, Volume 2, Homework Helper

15-4: TEKS Practice

  • 1. Think About the Process You want to simplify the following expression.

    fraction 13 to the eleventh , over 13 to the eighth end fraction

    • a. Which equation shows the property to use?

      • A. fraction a to the m , over a to the n end fraction . equals . a super m plus n end super

      • B. fraction a to the m , over a to the n end fraction . equals . a super m minus n end super

      • C. fraction a to the m , over a to the n end fraction . equals . a super m minus eh end super

      • D. fraction a to the m , over a to the n end fraction . equals . a super n minus m end super

    • b. Simplify the expression. Your answer should have only positive exponents.

  • 2. Use a property of exponents to simplify fraction 3 to the ninth , over 3 to the fifth end fraction . .

  • 3. Use a property of exponents to simplify fraction y to the twelfth , over y squared end fraction . .

  • 4. Think About the Process You want to simplify the following expression.

    open , 5 over c , close cubed

    • a. Which equation shows the property to use?

      • A. open , fraction a , over b end fraction , close to the n . equals . fraction n super a end super , over n to the b end fraction

      • B. open , fraction a , over b end fraction , close to the n . equals . fraction b to the n , over a to the n end fraction

      • C. open , fraction a , over b end fraction , close to the n . equals . fraction n to the b , over n super a end super end fraction

      • D. open , fraction a , over b end fraction , close to the n . equals . fraction a to the n , over b to the n end fraction

    • b. Simplify the expression. Your answer should have only positive exponents.

  • 5. Use a property of exponents to express open , y over 2 , close cubed as a fraction.

  • 6. Use properties of exponents to simplify open , fraction x to the fourth , over 7 end fraction , close squared . .

  • 7.  

    • a. Error Analysis Gino incorrectly said that fraction 9 to the eleventh , over 9 to the seventh end fraction . equals . fraction 0 to the eleventh , over 0 to the seventh end fraction . . Use a property of exponents to simplify fraction 9 to the eleventh , over 9 to the seventh end fraction correctly.

    • b. What was Gino's likely error?

      • A. He added the exponents.

      • B. He subtracted the exponents incorrectly.

      • C. He subtracted the bases instead of the exponents.

      • D. He subtracted the bases and the exponents.

  • 8.  

    • a. Reasoning Use a property of exponents to simplify fraction 30 , y to the twelfth , over 15 , y squared end fraction . .

    • b. For what values of y will the expression be negative?

  • 9.  

    • a. Writing Use a property of exponents to express open , x over 9 , close squared as a fraction.

    • b. If you had to do more work with this expression, would it be better to leave the denominator in exponential form or to expand it? Justify your answer.

  • 10. Use a property of exponents to simplify fraction negative 42 , x to the fifth , over 14 , x squared end fraction . .

  • 11. Bacteria The amount of bacteria in an infection n hours after taking medication is open , fraction 1 cubed , over x end fraction , close to the n . . Write a simplified expression that represents the amount of bacteria in an infection 3 hours after taking medication. Write your answer using exponential notation. Simplify your answer.

  • 12. Use properties of exponents to simplify open . fraction 5 , z to the sixth , over 6 end fraction . close squared . .

  • 13.  

    • a. Use properties of exponents to simplify fraction 7 to the thirteenth , over 7 to the eighth end fraction . .

    • b. Suppose the exponent in the denominator is greater than the exponent in the numerator. Describe a new property of exponents you could use to simplify the expression. Give two examples.

  • 14.  

    • a. Use properties of exponents to simplify open , fraction x to the sixth , over 7 end fraction , close cubed . .

    • b. Evaluate when x=1.


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Table of Contents

Digits, Grade 8, Volume 2, Homework Helper Unit D: Two-Dimensional Shapes Unit E: Measurement and Data Unit F: Personal Financial Literacy Unit G: Step-Up Lessons English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties