Asked by Jessica Strohmenger on May 25, 2024
Verified
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) 5
D) 10
E) 26
Simplify
The process of reducing an expression to its most compact or simplest form without changing its value.
Expression
An arrangement of symbols representing a value or denoting a mathematical operation, without an equality sign.
Exponents
Numbers that indicate how many times a base is to be multiplied by itself.
- Simplify expressions using rational exponents.
Verified Answer
HA
Himanshu AhlawatMay 28, 2024
Final Answer :
A
Explanation :
To simplify the expression 51/13514/13\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }514/1351/13 , use the rule of exponents that states aman=am−n\frac{a^m}{a^n} = a^{m-n}anam=am−n . Applying this rule here gives 5(1/13)−(14/13)=5−13/13=5−1=155^{(1/13) - (14/13)} = 5^{-13/13} = 5^{-1} = \frac{1}{5}5(1/13)−(14/13)=5−13/13=5−1=51 .
Learning Objectives
- Simplify expressions using rational exponents.