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Advanced Math / Equivalent expressions Difficulty: Easy

Which expression is equivalent to $left parenthesis m Superscript 4 Baseline q Superscript 4 Baseline z Superscript negative 1 Baseline right parenthesis left parenthesis m q Superscript 5 Baseline z cubed right parenthesis$ , where $m$ , $q$ , and $z$ are positive?

$m Superscript 4 Baseline q Superscript 20 Baseline z Superscript negative 3$

$m Superscript 5 Baseline q Superscript 9 Baseline z squared$

$m Superscript 6 Baseline q Superscript 8 Baseline z Superscript negative 1$

$m Superscript 20 Baseline q Superscript 12 Baseline z Superscript negative 2$

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Explanation

Choice B is correct. Applying the commutative property of multiplication, the expression $left parenthesis m Superscript 4 Baseline q Superscript 4 Baseline z Superscript negative 1 Baseline right parenthesis left parenthesis m q Superscript 5 Baseline z cubed right parenthesis$ can be rewritten as $left parenthesis m Superscript 4 Baseline m right parenthesis left parenthesis q Superscript 4 Baseline q Superscript 5 Baseline right parenthesis left parenthesis z Superscript negative 1 Baseline z cubed right parenthesis$ . For positive values of $x$ , $(x^{a}) (x^{b}) = x^{a + b}$ . Therefore, the expression $left parenthesis m Superscript 4 Baseline m right parenthesis left parenthesis q Superscript 4 Baseline q Superscript 5 Baseline right parenthesis left parenthesis z Superscript negative 1 Baseline z cubed right parenthesis$ can be rewritten as $(m^{4 + 1}) (q^{4 + 5}) (z^{- 1 + 3})$ , or $m Superscript 5 Baseline q Superscript 9 Baseline z squared$ .

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.