Question

Drag values to complete each equation.

Answer 1

`9^(-7)` and
`9^(-2)`

Explanation:

using the rules of exponents

•
`(a^m)^(n)` =
`a^(mn)`

•
`a^(m)` ×
`a^(n)` =
`a^((m+n))`

•
`(a^(m) )/(a^(n) )` =
`a^((m-n))`

given (
`9^(5)` ×
`9^(-9)` ) /
`9^(3)`

=
`(9^(5+(-9)) )/(9^(3) )` =
`(9^(-4) )/(9^(3) )` =
`9^(-4-3)` =
`9^(-7)`

given
`(9^4)^(3)` ×
`9^(-14)`

=
`9^(12)` ×
`9^(-14)`

=
`9^(12+(-14))` =
`9^(-2)`

Answer 2

Answer: The required values of the given expressions are

`(9^5.9^(-9))/(9^3)=9^(-7),~~~(9^4)^3.9^(-14)=9^(-2).`

Step-by-step explanation: We are given to find the values of the following expressions :

`E_1=(9^5.9^(-9))/(9^3)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\E_2=(9^4)^3.9^(-14)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

We will be using the following properties of exponents :

`(i)~x^a.x^b=x^(a+b),\\\\(ii)~(x^a)/(x^b)=x^(a-b)\\\\(iii)~(x^a)^b=x^(ab).`

From expression (i), we get

`E_1\\\\\\=(9^5.9^(-9))/(9^3)\\\\\\=(9^(5+(-9)))/(9^3)\\\\\\=(9^(-4))/(9^3)\\\\\\=9^(-4-3)\\\\=9^(-7)`

and from expression (ii), we get

`(9^4)^3.9^(-14)\\\\=9^(4*3).9^(-14)\\\\=9^(12).9^(-14)\\\\=9^(12+(-14))\\\\=9^(-2).`

Thus, the required values of the given expressions are

`(9^5.9^(-9))/(9^3)=9^(-7),~~~(9^4)^3.9^(-14)=9^(-2).`