(a) [tex]x^{-5}[/tex]
(b) [tex]3x^{-7}[/tex]
(c) [tex]$\frac{4}{3}x^4[/tex]
Solution:
To write each of the given expression in the form [tex]ax^n[/tex]:
(a) [tex]\frac{x^3}{x^8}[/tex]
Using exponential rule: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]$\frac{x^3}{x^8}=x^{3-8}[/tex]
[tex]$\frac{x^3}{x^8}=x^{-5}[/tex]
(b) [tex]\frac{6x}{2x^8}[/tex]
Divide numerator and denominator by the common factor 2, we get
[tex]$\frac{6x}{2x^8}=\frac{3x}{x^8}[/tex]
Using exponential rule: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]$=3x^{1-8}[/tex]
[tex]$\frac{6x}{2x^8} =3x^{-7}[/tex]
(c) [tex]\frac{28x^6}{21x^2}[/tex]
Divide numerator and denominator by the common factor 7, we get
[tex]$\frac{28x^6}{21x^2}=\frac{4x^6}{3x^2}[/tex]
Using exponential rule: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]$=\frac{4}{3}x^{6-2}[/tex]
[tex]$\frac{28x^6}{21x^2}=\frac{4}{3}x^4[/tex]
