Question

If $(81{)}^5÷(3^2{)}^5$$=3^k$ then value of $k$ is __.

Answer 1

Given, $(81{)}^5÷(3^2{)}^5$

We can write 81 as $3^4$

So, $(3^4{)}^5÷(3^2{)}^5$

= $(3{)}^{20}÷3^{10}$.... {as $(a^m{)}^n=a^{mn}$}

= $(3{)}^{20-10}$ .....{as $a^m÷a^n=a^{m-n}$}

= $(3{)}^{10}$

Comparing it with $3^k$,

The value of $k$ is $10$