Question

Fill in the blanks to make the statement true: ${(6/13)}^{10}÷[{(6/13)}^5{]}^2={(6/13)}^{---}$.

Answer 1

Simplify the given expression

To solve this we need the formula

$a^m÷a^n=a^{m-n}$

${\left(a^n\right)}^m=a^{m\times n}$

So by using the formula

$\begin{array}{rcl}(6/13{)}^{10}÷[{(6/13)}^5{]}^2& =& (6/13{)}^{10}÷{(6/13)}^{5\times 2}\\ & =& (6/13{)}^{10}÷{(6/13)}^{10}\\ & =& (6/13{)}^{10-10}\\ & =& (6/13{)}^0\end{array}$

Hence the required statement is ${(6/13)}^{10}÷[{(6/13)}^5{]}^2={(6/13)}^0$.