Simplify the expression 5 6 u 9 v 9 5 8 u 9 v 3 \frac { 5 ^ { 6 } u ^ { 9 } v ^ { 9 } } { 5 ^ { 8 } u ^ { 9 } v ^ { 3 } } 5 8 u 9 v 3 5 6 u 9 v 9 . Assume that neither u nor v is zero.A) u v 6 10 \frac { u v ^ { 6 } } { 10 } 10 u v 6 B) v 6 25 \frac { v ^ { 6 } } { 25 } 25 v 6 C) v 6 10 \frac { v ^ { 6 } } { 10 } 10 v 6 D) v 3 25 \frac { v ^ { 3 } } { 25 } 25 v 3 E) u v 3 10 \frac { u v ^ { 3 } } { 10 } 10 u v 3

Question

Simplify the expression   5 6 u 9 v 9 5 8 u 9 v 3 \frac { 5 ^ { 6 } u ^ { 9 } v ^ { 9 } } { 5 ^ { 8 } u ^ { 9 } v ^ { 3 } } 5 8 u 9 v 3 5 6 u 9 v 9 ​   . Assume that neither u nor v is zero.A)    u v 6 10 \frac { u v ^ { 6 } } { 10 } 10 u v 6 ​ B)    v 6 25 \frac { v ^ { 6 } } { 25 } 25 v 6 ​ C)    v 6 10 \frac { v ^ { 6 } } { 10 } 10 v 6 ​ D)    v 3 25 \frac { v ^ { 3 } } { 25 } 25 v 3 ​ E)    u v 3 10 \frac { u v ^ { 3 } } { 10 } 10 u v 3 ​

Perla Martos · Accepted Answer

Final Answer : B, Explanation :   To simplify the expression, subtract the exponents of like bases in the numerator and denominator:   5 6 − 8 = 5 − 2 5^{6-8} = 5^{-2} 5 6 − 8 = 5 − 2  ,   u 9 − 9 = u 0 = 1 u^{9-9} = u^0 = 1 u 9 − 9 = u 0 = 1  , and   v 9 − 3 = v 6 v^{9-3} = v^6 v 9 − 3 = v 6  . This results in   1 5 2 ⋅ v 6 = v 6 25 \frac{1}{5^2} \cdot v^6 = \frac{v^6}{25} 5 2 1 ​ ⋅ v 6 = 25 v 6 ​  .

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