Explanation Given: The expression 3 k 2 ⋅ ( 4 k − 3 ) − 1 4 1 / 2 ⋅ k 7 / 2 . Definition of negative exponent: If a is any nonzero real number and n is a positive integer, then a − n = 1 a n . Definition of a m / n : “For all real numbers a for which the indicated roots exist, and for any rational number m / n , a m / n = ( a 1 / n ) m ”. Property used: (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. Calculation: Apply the definition of a m / n and simplify the terms of the given expression. 3 k 2 ⋅ ( 4 k − 3 ) − 1 4 1 / 2 ⋅ k 7 / 2 = 3 k 2 ⋅ ( 4 − 1 ) ⋅ k ( − 3 ) ( − 1 ) ( 2 × 2 ) 1 / 2 ⋅ k 7 / 2 = 3 k 2 ⋅ 4 − 1 ⋅ k 3 ( 2 2 ) 1 / 2 ⋅ k 7 / 2 = 3 k 2 ⋅ 4 − 1 ⋅ k 3 2 ⋅ k 7 / 2 Group the like terms of the given expression, 3 k 2 ⋅ ( 4 k − 3 ) − 1 4 1 / 2 ⋅ k 7 / 2 = 3 ⋅ 4 − 1 ⋅ k 2 ⋅ k 3 2 ⋅ k

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

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

Publisher: Pearson Education

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Chapter R.6, Problem 45E

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To simplify: The expression 3k2⋅(4k−3)−141/2⋅k7/2 and write answer with only positive exponents.

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Chapter R.6, Problem 44E

Chapter R.6, Problem 46E

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Chapter R Solutions

Calculus with Applications Books a la Carte 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 k 2 ⋅ ( 4 k − 3 ) − 1 4 1 / 2 ⋅ k 7 / 2 and write answer with only positive exponents.

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To simplify: The expression 3k2⋅(4k−3)−141/2⋅k7/2 and write answer with only positive exponents.

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Chapter R Solutions