(A) Explanation Definition used: Rational exponents: b m n = { ( b 1 n ) m = ( b n ) m ( b m ) 1 n = b m n a n d b − m n = 1 b m n ( b ≠ 0 ) Here m and n are natural numbers without common prime factors, b is a real number, and b is non-negative when n is even. Calculation: The given expression is 2 c 1 4 ( 5 c 3 − c 3 4 ) (B) To determine To simplify: The expression ( 7 x 1 2 − y 1 2 ) ( 2 x 1 2 + 3 y 1 2 ) and express the answer using positive exponents.

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Chapter A.6, Problem 4MP

(A)

To determine

To multiply: The expression 2c14(5c3−c34) and express the answer using positive exponents.

(B)

To determine

To simplify: The expression (7x12−y12)(2x12+3y12) and express the answer using positive exponents.

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Chapter A.6, Problem 3MP

Chapter A.6, Problem 5MP

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To multiply: The expression 2 c 1 4 ( 5 c 3 − c 3 4 ) and express the answer using positive exponents.

Solution Summary: The author explains how to simplify the expression using positive exponents: m and n are natural numbers without common prime factors, b is a real number.