which expression is equivalent to $(m^{3/5})^{1/5}$?\na. $m^{2/5}$\nb. $m^{4/5}$\nc. $m^{3/25}$\nd. $m^{1/3}$

Explanation:

Step1: Aplicar la regla de potencia de una potencia

$(a^m)^n=a^{m\times n}$ Así, $(m^{\frac{3}{5}})^{\frac{1}{5}} = m^{\frac{3}{5}\times\frac{1}{5}}$

Step2: Calcular el producto de fracciones

$\frac{3}{5}\times\frac{1}{5}=\frac{3\times1}{5\times5}=\frac{3}{25}$ Entonces, $(m^{\frac{3}{5}})^{\frac{1}{5}}=m^{\frac{3}{25}}$

Answer:

C. $m^{\frac{3}{25}}$