Question

Write the proper numbers in the boxes.

(2) ${\left(\frac{6}{11}\right)}^4\times \left(\frac{6}{11}\right)={\left(\frac{6}{11}\right)}^{\boxed{}}$

Answer 1

${\left(\frac{6}{11}\right)}^4\times \left(\frac{6}{11}\right)={\left(\frac{6}{11}\right)}^{\boxed{}}$
Consider ${\left(\frac{6}{11}\right)}^4\times \left(\frac{6}{11}\right)$
$$\begin{gathered} ={\left(\frac{6}{11}\right)}^4\times {\left(\frac{6}{11}\right)}^1 \\ ={\left(\frac{6}{11}\right)}^{4+1}\left(a^m\times a^n=a^{m+n}\right) \\ ={\left(\frac{6}{11}\right)}^{\boxed{5}} \end{gathered}$$