1. Simplify 8^{4}·8^{2} to an equivalent exponential expression.
2. Simplify the expression (4x ^{5})(5x ^{6}).
3. Simplify the expression.
(−7y ^{3})(5y ^{2})
4. Think About the Process
a. What do you do to find the power of a power?
A. Divide the exponents.
B. Subtract the exponents.
C. Add the exponents.
D. Multiply the exponents.
b. Simplify the expression (x ^{3})^{7}.
5. Simplify the expression (6^{9})^{8}.
6. Simplify the expression (x ^{17})^{2}.
7. Use the properties of exponents to rewrite the expression (3·6)^{2}.
8. Simplify the expression (3x ^{6})^{2}.
9. Think About the Process
a. How do you multiply powers that have the same base?
A. Divide the exponents.
B. Subtract the exponents.
C. Multiply the exponents.
D. Add the exponents.
b. Simplify the expression x ^{7}·x^{5}·x^{4}.
10.
a. Reasoning Simplify x ^{11}·x^{9} and x ^{12}·x^{8} to equivalent exponential expressions.
b. Does x ^{11}·x^{9}=x^{12}·x^{8} for all values of x?
c. Give another way to justify your answer without doing any arithmetic.
11.
a. Multiple Representations Simplify the expression 3^{4}·3^{5}. Write your answer using exponential notation. Simplify your answer.
b. What are three other ways to write the product as the multiplication of two powers?
A. 3^{5}·3^{6}, 3^{5}·3^{7}, 3^{2}·3^{4}
B. 3^{4}·3^{4}, 3^{4}·3^{6}, 3^{4}·3^{7}
C. 3^{5}·3^{5}, 3^{2}·3^{5}, 3^{3}·3^{5}
D. 3^{5}·3^{4}, 3^{3}·3^{6}, 3^{2}·3^{7}
12. Simplify the expression. Choose the correct answer below.
(3fg)^{9}
A. (3fg)^{9}=19,683fg^{9}
B. (3fg)^{9}=59,049g^{10}f^{10}
C. (3fg)^{9}=6,561g^{8}f^{8}
D. (3fg)^{9}=19,683f^{9}g^{9}
13. Error Analysis Your teacher asks the class to evaluate the expression (2^{3})^{1}. Your classmate gives an incorrect answer of 16.
a. Evaluate the expression.
b. What was the likely error?
A. Your classmate divided the exponents.
B. Your classmate multiplied the exponents.
C. Your classmate added the exponents.
D. Your classmate subtracted the exponents.
14.
a. Writing Use a property of exponents to write (3b)^{5} as a product of powers.
b. Describe the property of exponents that you used. In words, what does the power of a product equal?
15. Flow Rate A company manufactures faucets. It uses the expression (4y ^{6})^{3} mm/s to calculate the maximum flow rate of water flowing out a spout with area y ^{6} mm^{2}. Use a property of exponents to simplify the flow-rate expression. Write your answer using exponential notation. Simplify your answer.
16.
a. Simplify the expression [(−20)^{5}]^{3}.
b. Is the number positive or negative? Explain how you know.
17.
a. Simplify the expression 3(x^{8})^{3}+3(x^{2})^{12}.
b. Give the values of x for which the expression is positive. Explain how you know.
c. Give the values of x for which the expression is negative. Explain how you know.