Question

Look at pic and answer pls

Answer 1

(a)
`x^(-5)`

(b)
`3x^(-7)`

(c)
`$(4)/(3)x^4`

Solution:

To write each of the given expression in the form
`ax^n`:

(a)
`(x^3)/(x^8)`

Using exponential rule:
`(a^x)/(a^y)=a^(x-y)`

`$(x^3)/(x^8)=x^(3-8)`

`$(x^3)/(x^8)=x^(-5)`

(b)
`(6x)/(2x^8)`

Divide numerator and denominator by the common factor 2, we get

`$(6x)/(2x^8)=(3x)/(x^8)`

Using exponential rule:
`(a^x)/(a^y)=a^(x-y)`

`$=3x^(1-8)`

`$(6x)/(2x^8) =3x^(-7)`

(c)
`(28x^6)/(21x^2)`

Divide numerator and denominator by the common factor 7, we get

`$(28x^6)/(21x^2)=(4x^6)/(3x^2)`

Using exponential rule:
`(a^x)/(a^y)=a^(x-y)`

`$=(4)/(3)x^(6-2)`

`$(28x^6)/(21x^2)=(4)/(3)x^4`