Question

3. Which inequalities show a correct relationship between expressions?

a. 32^3 < 16^4
b. 27^3> 81^4
C. 9^3 < 3^5
d. 8^4 > 32^2

Answer 1

Answer: a and d

Explanation:

First of all, we need to make a analysis of each letters:

a. factoring 32 = 2.2.2.2.2 =
`2^(5)`

`2^(5)^(3) = 2^(15)`

then,

16 =
`2^(4)`

but
`2^(4)^(4) =2^(16)`

in conclusion that, this inequality is correct

b. 27 =
`3^(3)`

this first situation is equal to
`3^(9)`

the second situation is:

81 =
`3^(4)`

and
`3^(4)^(4) = 3^(16)`

it's a mistake.

c. factoring 9:
`9 = 3^(3)`

`3^(9)` <
`3^(5)`

it's wrong.

d. factoring 8 =
`2^(3)`

factoring 32 =
`2^(5)`

`2^(12)` >
`2^(10)`

This is true.

Finally.. our correct answers is a and d.