sat suite question viewer

Advanced Math / Equivalent expressions Difficulty: Medium

$the cube root of x to the power 3, times y to the power 6, end root$

Which of the following expressions is equivalent to the expression above?

A. $y squared$

B. $x times y squared$

C. $y cubed$

D. $x times y cubed$

Back question 23 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 B is correct. One of the properties of radicals is $the nth root of a times b, end root, equals the nth root of a, end root, times the nth root of b, end root$ . Thus, the given expression can be rewritten as $the cube root of x cubed, end root, times the cube root of y to the power 6, end root$ . Simplifying by taking the cube root of each part gives x¹⋅ y², or xy².

Choices A, C, and D are incorrect and may be the result of incorrect application of the properties of exponents and radicals.