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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