if $$\left(\frac{32}{243}\right)^k = \frac{8}{27}$$, then k = ___________.​

Correct option is C

Given:

​$$\left(\frac{32}{243}\right)^k = \frac{8}{27}$$​​

Formula Used:

​$$(x^a)^b = x^{ab}$$​​

Solution:

​$$\left(\frac{32}{243}\right)^k = \frac{8}{27}$$​​

​$$\left(\frac{(2)^5}{(3)^5}\right)^k = \frac{(2)^3}{(3)^3}$$​​

​$$\left(\frac{2}{3}\right)^{5k} = \left(\frac{2}{3}\right)^3$$​​

When bases are equal we equate the powers, hence:

5k = 3

​$$k=\frac{3}{5}$$​​