Answer: Expression as a power of the number a is given as
[tex]a^{-2}[/tex]
Explanation:
Since we have given that
[tex]{(\frac{a^3\times a}{a^2}})^{-1}[/tex]
First we use the exponential law i.e.
[tex]a^m\times a^n=a^{m+n}[/tex]
So, our expression becomes,
[tex]{(\frac{a^{ 3+1}}{a^2})^{-1}[/tex]
[tex]{(\frac{a^4}{a^2}})^{-1}[/tex]
Now, we'll use the exponential law i.e.
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
So, it becomes,
[tex]{(a^{4-2})^{-1}[/tex]
[tex](a^2)^{-1}[/tex]
Now, we'll use the exponential law i.e.
[tex](a^m)^n=a^{mn}[/tex]
Hence, our expression becomes,
[tex]a^{-2}[/tex]
