Question which-

2.4 Equivalent Expressions - Simplifying rational expressions
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Which expression is equivalent to m4q4z-1mq5z3, where m , q , and z are positive?

A.

m4q20z-3

B.

m 5 q 9 z 2

C.

m6q8z-1

D.

m20q12z-2

Which expression is equivalent to m 4 q 4 z - 1 m q 5 z

Medium-difficulty · SAT Math · Equivalent Expressions — Simplifying rational expressions. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice B is correct. Applying the commutative property of multipliion, the expression m4q4z-1mq5z3 can be rewritten as m4mq4q5z-1z3. For positive values of x , xaxb=xa+b. Therefore, the expression m4mq4q5z-1z3 can be rewritten as m4+1q4+5z-1+3, or m5q9z2.

Choice A is incorrect and may result from multiplying, not adding, the exponents.

Choice C is incorrect and may result from conceptual or calculation errors. 

Choice D is incorrect and may result from conceptual or calculation errors.