Question

Represent the following expressions as a power of the number a (a≠0):
(a^3*a/a^2)^-1

Answer 1

Answer: Expression as a power of the number a is given as

`a^(-2)`

Step-by-step explanation:

Since we have given that

`{((a^3* a)/(a^2)})^(-1)`

First we use the exponential law i.e.

`a^m* a^n=a^(m+n)`

So, our expression becomes,

`{((a^( 3+1))/(a^2))^(-1)`

`{((a^4)/(a^2)})^(-1)`

Now, we'll use the exponential law i.e.

`(a^m)/(a^n)=a^(m-n)`

So, it becomes,

`{(a^(4-2))^(-1)`

`(a^2)^(-1)`

Now, we'll use the exponential law i.e.

`(a^m)^n=a^(mn)`

Hence, our expression becomes,

`a^(-2)`