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.