sat suite question viewer

Advanced Math / Equivalent expressions Difficulty: Medium

Which expression represents the product of $left parenthesis x Superscript negative 6 Baseline y cubed z Superscript 5 Baseline right parenthesis$ and $(x^{4} z^{5} + y^{8} z^{- 7})$ ?

$x^{- 2} z^{10} + y^{11} z^{- 2}$

$x^{- 2} z^{10} + x^{- 6} z^{- 2}$

$x^{- 2} y^{3} z^{10} + y^{8} z^{- 7}$

$x^{- 2} y^{3} z^{10} + x^{- 6} y^{11} z^{- 2}$

Back question 59 of 102 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

Explanation

Choice D is correct. The product of $left parenthesis x Superscript negative 6 Baseline y cubed z Superscript 5 Baseline right parenthesis$ and $(x^{4} z^{5} + y^{8} z^{- 7})$ can be represented by the expression $(x^{- 6} y^{3} z^{5}) (x^{4} z^{5} + y^{8} z^{- 7})$ . Applying the distributive property to this expression yields $(x^{- 6} y^{3} z^{5}) (x^{4} z^{5}) + (x^{- 6} y^{3} z^{5}) (y^{8} z^{- 7})$ , or $x^{- 6} x^{4} y^{3} z^{5} z^{5} + x^{- 6} y^{3} y^{8} z^{5} z^{- 7}$ . This expression is equivalent to $x^{- 6 + 4} y^{3} z^{5 + 5} + x^{- 6} y^{3 + 8} z^{5 - 7}$ , or $x^{- 2} y^{3} z^{10} + x^{- 6} y^{11} z^{- 2}$ .

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

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

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