Explanation Given: The expression ( 3 z 2 ) − 1 z 5 . Property used: Negative exponents : If a is any nonzero real number and n is a positive integer, then a − n = 1 a n . 1. For any real number a , a m ⋅ a n = a m + n , where m and n are any integers. 2. For any real number a , a m a n = a m − n , where m and n are any integers. 3. For any real number a , ( a m ) n = a m n , where m and n are any integers. 4. For any real numbers a and b , ( a b ) m = a m ⋅ b m , where m and n are any integers. Calculation: From the numerator of the given expression ( 3 z 2 ) − 1 , it is observed that a = 3 , b = z 2 , and m = − 1 . By the property 4 stated above, ( 3 z 2 ) − 1 = ( 3 ) − 1 ⋅ ( z 2 ) − 1 . Apply the properties and simplify the terms. ( 3 z 2 ) − 1 = 1 3 ⋅ ( z 2 ) − 1 [ By negative exponent, a − n = 1 a n ] = 1 3 ⋅ z ( 2 ) ⋅ ( − 1 )

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter R.6, Problem 16E

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To simplify: The expression (3z2)−1z5 and write the answer with only positive exponents.

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Chapter R.6, Problem 15E

Chapter R.6, Problem 17E

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Chapter R Solutions

Calculus with Applications (11th Edition)

Ch. R.1 - YOUR TURN 1 Perform the operation Ch. R.1 - YOUR TURN 2 Perform the operation . Ch. R.1 - Prob. 3YT Ch. R.1 - Prob. 4YT Ch. R.1 - Perform the indicated operations. 1. Ch. R.1 - Prob. 2E Ch. R.1 - Prob. 3E Ch. R.1 - Prob. 4E Ch. R.1 - Perform the indicated operations. 5. Ch. R.1 - Perform the indicated operations. 6.

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The expression ( 3 z 2 ) − 1 z 5 and write the answer with only positive exponents.

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To simplify: The expression (3z2)−1z5 and write the answer with only positive exponents.

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Chapter R Solutions