Simplify the expression 5 1 / 13 5 14 / 13 \frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } } 5 14/13 5 1/13 .A) 1 5 \frac{1}{5} 5 1 B) 1 26 \frac { 1 } { 26 } 26 1 C) 5D) 10E) 26

Question

Simplify the expression   5 1 / 13 5 14 / 13 \frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } } 5 14/13 5 1/13 ​   .A)    1 5  \frac{1}{5}  5 1 ​ B)    1 26 \frac { 1 } { 26 } 26 1 ​ C)  5D)  10E)  26

Himanshu Ahlawat · Accepted Answer

Final Answer : A, Explanation :   To simplify the expression   5 1 / 13 5 14 / 13 \frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } } 5 14/13 5 1/13 ​  , use the rule of exponents that states   a m a n = a m − n \frac{a^m}{a^n} = a^{m-n} a n a m ​ = a m − n  . Applying this rule here gives   5 ( 1 / 13 ) − ( 14 / 13 ) = 5 − 13 / 13 = 5 − 1 = 1 5 5^{(1/13) - (14/13)} = 5^{-13/13} = 5^{-1} = \frac{1}{5} 5 ( 1/13 ) − ( 14/13 ) = 5 − 13/13 = 5 − 1 = 5 1 ​  .

Simplify the expression $51/13514/13\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }$ .

A) $\frac{1}{5}$
B) $126\frac { 1 } { 26 }$
C) 5
D) 10
E) 26

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Simplify the expression 51/13514/13\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }514/1351/13​ .A) 15 \frac{1}{5} 51​ B) 126\frac { 1 } { 26 }261​ C) 5D) 10E) 26

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Learning Objectives

Related questions

Simplify the expression $51/13514/13\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }$ .

A) $\frac{1}{5}$
B) $126\frac { 1 } { 26 }$
C) 5
D) 10
E) 26