Question

Find the value of y if : $(100{)}^2\times (10{)}^5=(1000{)}^y$

Answer 1

Consider the given equation,

${\left(100\right)}^2\times {\left(10\right)}^5={\left(100\right)}^y$

${\left({10}^2\right)}^2\times {\left(10\right)}^5={\left(10\right)}^y$

$\left({10}^4\right)\times {\left(10\right)}^5={\left(10\right)}^y$

$\left({10}^{4+5}\right)={\left(10\right)}^y$

${10}^9={10}^y$

$y=9$

Hence, this is the answer.