Question

50 points

Solve and post answer, I will name you brinislst

Answer 1

27. Yes

28. No

29.
`2^(-3)`

30.
`2 ^(-7)` ·
`2^(-4)`

`(1)/(2^(11) )`

Explanation:

27.
`(3^2)^(-3)` =
`9^(-3)` =
`(1)/(9)` ×
`(1)/(9)` ×
`(1)/(9)` =
`(1)/(729)`

`(3^3)^(-2)` =
`27^(-2)` =
`(1)/(27)` ×
`(1)/(27)` =
`(1)/(729)`

Both expressions have a negative exponent but have the same base making the expressions equivalent

28.
`3^2` ·
`3^(-3)` = 3 × 3 = 9

`3^(-3)` =
`(1)/(3)` ×
`(1)/(3)` ×
`(1)/(3)` =
`(1)/(27)`

9 ·
`(1)/(27)` =
`(1)/(3)`

`3^(3)` ·
`3^(-2)` = 3 × 3 × 3 = 27

`3^(-2)` =
`(1)/(3)` ×
`(1)/(3)` =
`(1)/(9)`

27 ×
`(1)/(9)` = 3

Both expressions result in different answers because the exponents are different

29.

Area =
`l` ×
`w`

`2^(-4)` =
`2^(-1)` ×
`w`

`w=(2^(-4) )/(2^(-1) )`

`w=(1)/(8)`

This is NOT a expression!

In order to write it as an expression, simply know what number multiplied by itself 3 times equal
`(1)/(8)`

s × s × s =
`(1)/(8)` (s represents the number)

`(1)/(2)` ×
`(1)/(2)` ×
`(1)/(2)` =
`(1)/(8)`

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