Perform the operation. Write the answer without negative exponents. $\frac { 5 ^ { - \frac { 1 } { 5 } } \cdot 5 ^ { \frac { 4 } { 5 } } } { 5 ^ { \frac { 7 } { 5 } } }$
A) $\frac { 1 } { 25 ^ { \frac { 3 } { 5 } } }$
B) $5 ^ { \frac { 4 } { 5 } }$
C) $\frac { 1 } { 5 }$
D) $\frac { 1 } { 5 ^ { \frac { 4 } { 5 } } }$

Question

Quizplus · Accepted Answer

To solve the expression, use the laws of exponents. Combine the exponents in the numerator by adding them: $-\frac{1}{5} + \frac{4}{5} = \frac{3}{5}$. Then, subtract the exponent in the denominator: $\frac{3}{5} - \frac{7}{5} = -\frac{4}{5}$. This results in $5^{-\frac{4}{5}}$, which is equivalent to $\frac{1}{5^{\frac{4}{5}}}$.

Perform the Operation 5−15⋅545575\frac { 5 ^ { - \frac { 1 } { 5 } } \cdot 5 ^ { \frac { 4 } { 5 } } } { 5 ^ { \frac { 7 } { 5 } } }557​5−51​⋅554​​

Perform the Operation $\frac { 5 ^ { - \frac { 1 } { 5 } } \cdot 5 ^ { \frac { 4 } { 5 } } } { 5 ^ { \frac { 7 } { 5 } } }$