Evaluate the expression.
-$$\left( - \frac { 1 } { 3125 } \right) ^ { - 2 / 5 }$$
A) not a real number
B) $\frac { 1 } { 25 }$
C) $298,023,223,876,953,152$
D) 25

Question

Quizplus · Accepted Answer

The expression $\left( - \frac { 1 } { 3125 } \right) ^ { - 2 / 5 }$ simplifies to $25$ because $-\frac{1}{3125} = -5^{-5}$, and when raised to the power of $-2/5$, the negative exponent inverts the base and the fraction exponent effectively takes the fifth root and then squares the result, leading to $5^2 = 25$. Negative bases with rational exponents that result in real numbers indicate that the operation is valid under the given conditions, hence the result is a real number, specifically 25.

Evaluate the Expression (−13125)−2/5\left( - \frac { 1 } { 3125 } \right) ^ { - 2 / 5 }(−31251​)−2/5

Evaluate the Expression $\left( - \frac { 1 } { 3125 } \right) ^ { - 2 / 5 }$