ANSWER
[tex](-6.1)^2[/tex]EXPLANATION
We are given the expression:
[tex]\frac{(-6.1)^{11}}{(-6.1)^7\cdot\text{ }\mleft(-6.1\mright)^2}[/tex]Since each of the terms have the same base (-6.1), we will simplify this by applying the law of indices.
When two terms have the same base but different powers:
=> If they are multiplying one another, we add the powers;
=> If one divides the other, subtract the power of the denominator from the numerator.
That is:
[tex]\begin{gathered} \frac{(-6.1)^{11}}{(-6.1)^7\cdot(-6.1)^2}\text{ = }\frac{(-6.1)^{11}}{(-6.1)^{7\text{ + 2}}} \\ \Rightarrow\text{ }\frac{(-6.1)^{11}}{(-6.1)^9} \\ \Rightarrow(-6.1)^{11\text{ - 9}} \\ \Rightarrow(-6.1)^2 \end{gathered}[/tex]That is the simplified expression.
