### 15-3: TEKS Practice

• 1. Simplify 84·82 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.

• D. Multiply the exponents.

• b. Simplify the expression (x 3)7.

• 5. Simplify the expression (69)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.

• b. Simplify the expression x 7·x5·x4.

• 10.

• a. Reasoning Simplify x 11·x9 and x 12·x8 to equivalent exponential expressions.

• b. Does x 11·x9=x12·x8 for all values of x?

• c. Give another way to justify your answer without doing any arithmetic.

• 11.

• b. What are three other ways to write the product as the multiplication of two powers?

• A. 35·36, 35·37, 32·34

• B. 34·34, 34·36, 34·37

• C. 35·35, 32·35, 33·35

• D. 35·34, 33·36, 32·37

• 12. Simplify the expression. Choose the correct answer below.

(3fg)9

• A. (3fg)9=19,683fg9

• B. (3fg)9=59,049g10f10

• C. (3fg)9=6,561g8f8

• D. (3fg)9=19,683f9g9

• a. Evaluate the expression.

• b. What was the likely error?

• A. Your classmate divided the exponents.

• B. Your classmate multiplied 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 mm2. 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(x8)3+3(x2)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.

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