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

Step-by-step 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.