Question

Need ASAP

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

9
3
1/3

Answer 1

Power with an integer exponent.

Definition of a power with a natural exponent:

`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)`

also

`a^1=a\\\\a^0=1`

Definition of a power with an integer negative exponent:

`a^(-1)=(1)/(a)\\\\a^(-2)=(1)/(a^2)\\\\a^(-3)=(1)/(a^3)\\\vdots\\a^(-n)=(1)/(a^n)\\\\n\in\mathbb{N}`

`h^(-2)g\\\\h=3,\ g=27`

METHOD 1:

`3^(-2)\cdot27=(1)/(3^2)\cdot27=(27)/(9)=3`

METHOD 2:

`3^(-2)\cdot27=3^(-2)\cdot3^3`

use
`a^n\cdot a^m=a^(n+m)`

`=3^(-2+3)=3^1=3`

Answer: 3

Answer 2

3

Explanation:

h^-2 g

h= 3 and g = 27

(3) ^-2 (27)

1/3^2 (27)

1/9 *27

27/9

3