Question

[4/5]-6×[4/5]3=[4/5]2m+1​

Answer 1

$Given \: \Big(\frac{4}{5}\Big)^{-6} \times \Big(\frac{4}{5}\Big)^{3} = \Big(\frac{4}{5}\Big)^{2m+1}$

$\implies \Big(\frac{4}{5}\Big)^{-6+3} = \Big(\frac{4}{5}\Big)^{2m+1}$

/* By Exponential Law */

$\boxed{\pink{ a^{m} \times a^{n} = a^{m + n }}}$

$\implies \Big(\frac{4}{5}\Big)^{-3} = \Big(\frac{4}{5}\Big)^{2m+1}$

$\implies -3 = 2m+1$

$\boxed{\pink { If \: a^{m} = a^{n} \implies m = n }}$

$\implies -3 - 1 = 2m$

$\implies 2m = -4$

$\implies m = \frac{-4 }{2}$

$\implies m = -2$

Therefore.,

$\red{ Value \: of \: m }\green { = -2 }$

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