which is equivalent to $243^{\frac{2}{5}}$?\n3\n6\n9\n12

Explanation:

Step1: Rewrite 243 as a power of 3

$243 = 3^5$, so $243^{\frac{2}{5}}=(3^5)^{\frac{2}{5}}$

Step2: Apply power - of - a - power rule

According to the rule $(a^m)^n=a^{mn}$, we have $(3^5)^{\frac{2}{5}}=3^{5\times\frac{2}{5}}$

Step3: Calculate the exponent

$5\times\frac{2}{5}=2$, so $3^{5\times\frac{2}{5}} = 3^2$

Step4: Evaluate $3^2$

$3^2=9$

Answer:

C. 9