The value of m such that ( \frac{2}{9})^{3}\times( \frac{4}{81})^{-6}=( \frac{2}{9})^{2m-1} is

CTET 2 Math and Science Feb 2016 Paper

Question : 32 of 120

Marks: +1, -0

The value of m such that

(\;\;{2}/{9})^{3}×(\;\;{4}/{81})^{-6}=(\;\;{2}/{9})^{2m-1}

Solution:

(\;\;{2}/{9})^{3}×(\;\;{4}/{81})^{-6}=(\;\;{2}/{9})^{2m-1}

⇒(\;\;{2}/{9})^{3}×(\;\;{2}/{9})^{2×(-6)}=(\;\;{2}/{9})^{2m-1}

⇒(\;\;{2}/{9})^{3}×(\;\;{2}/{9})^{-12}=(\;\;{2}/{9})^{2{m}-1}

⇒(\;\;{2}/{9})^{3+(-12)}=(\;\;{2}/{9})^{2m-1}

⇒2m-1=-9

⇒2m=-9+1=-8

∴{m}=\;\;{-8}/{2}=-4

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