Power with an integer exponent.
Definition of a power with a natural exponent:
[tex]a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]
also
[tex]a^1=a\\\\a^0=1[/tex]
Definition of a power with an integer negative exponent:
[tex]a^{-1}=\dfrac{1}{a}\\\\a^{-2}=\dfrac{1}{a^2}\\\\a^{-3}=\dfrac{1}{a^3}\\\vdots\\a^{-n}=\dfrac{1}{a^n}\\\\n\in\mathbb{N}[/tex]
[tex]h^{-2}g\\\\h=3,\ g=27[/tex]
METHOD 1:
[tex]3^{-2}\cdot27=\dfrac{1}{3^2}\cdot27=\dfrac{27}{9}=3[/tex]
METHOD 2:
[tex]3^{-2}\cdot27=3^{-2}\cdot3^3[/tex]
use [tex]a^n\cdot a^m=a^{n+m}[/tex]
[tex]=3^{-2+3}=3^1=3[/tex]
Answer: 3
