e x + 6 e x \frac { e ^ { x + 6 } } { e ^ { x } } e x e x + 6 A) 1 + e 6 − x 1 + e ^ { 6 - x } 1 + e 6 − x B) e 6 e ^ { 6 } e 6 C) e 1 + 6 x e^{1 + \frac { 6 } { x }} e 1 + x 6 D) 1 + e 6 x 1 + e ^ { \frac { 6 } { x } } 1 + e x 6 E) cannot be simplified

Question

e x + 6 e x \frac { e ^ { x + 6 } } { e ^ { x } } e x e x + 6 ​ A)    1 + e 6 − x 1 + e ^ { 6 - x } 1 + e 6 − x B)    e 6 e ^ { 6 } e 6 C)    e 1 + 6 x e^{1 + \frac { 6 } { x }} e 1 + x 6 ​ D)    1 + e 6 x 1 + e ^ { \frac { 6 } { x } } 1 + e x 6 ​ E) cannot be simplified

Gavin Worland · Accepted Answer

Final Answer : B, Explanation :   The expression simplifies using the exponent rule   e a / e b = e a − b e^{a}/e^{b} = e^{a-b} e a / e b = e a − b  , resulting in   e ( x + 6 ) − x = e 6 e^{(x+6)-x} = e^{6} e ( x + 6 ) − x = e 6  .

$ex+6ex\frac { e ^ { x + 6 } } { e ^ { x } }$

A) $1 + e ^ { 6 - x }$
B) $e ^ { 6 }$
C) $e1+6xe^{1 + \frac { 6 } { x }}$
D) $\frac { 6 } { x } }$
E) cannot be simplified

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Learning Objectives

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ex+6ex\frac { e ^ { x + 6 } } { e ^ { x } }exex+6​ A) 1+e6−x1 + e ^ { 6 - x }1+e6−x B) e6e ^ { 6 }e6 C) e1+6xe^{1 + \frac { 6 } { x }}e1+x6​ D) 1+e6x1 + e ^ { \frac { 6 } { x } }1+ex6​ E) cannot be simplified

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Learning Objectives

Related questions

$ex+6ex\frac { e ^ { x + 6 } } { e ^ { x } }$

A) $1 + e ^ { 6 - x }$
B) $e ^ { 6 }$
C) $e1+6xe^{1 + \frac { 6 } { x }}$
D) $\frac { 6 } { x } }$
E) cannot be simplified