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Evaluate h^-2 g for h = 3 and g = 27.

9
3
1/3

Sagot :

wegnerkolmp2741o

Answer:

3

Step-by-step explanation:

h^-2 g

h= 3 and g = 27

(3) ^-2 (27)

1/3^2 (27)

1/9 *27

27/9

3

gmany

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

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