Question

(3/5)^2m * (3/5) ^6 * 3/5 = (3/5) ^13 * (3/5)^6?

Answer 1

Answer:

$( { \frac{3}{5}) }^{2m} \times ({ \frac{3}{5} )}^{6} \times \frac{3}{5} = ({ \frac{3}{5}) }^{13} \times ({ \frac{3}{5} )}^{6} \\ \\ ({ \frac{3}{5}) }^{2m +6 + 1} = ({ \frac{3}{5}) }^{13 + 6} \\ \\ ({ \frac{3}{5} )}^{2m + 7} = ({ \frac{3}{5} )}^{19} \\ \\ now \: we \: solve \: powers \: as \: base \: is \\ \: same \: in \: both \: lhs \: and \: rhs. \\ \\ 2m + 7 = 19 \\ \\ 2m = 19 - 7 \\ \\ 2m = 12 \\ \\ m = \frac{12}{2} \\ \\ m = 6$

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