Let's evaluate the given exponential expressions step-by-step and determine which one is correctly evaluated:
a.) [tex]\( 12^3 = 36 \)[/tex]
Calculate [tex]\( 12^3 \)[/tex]:
[tex]\[ 12^3 = 12 \times 12 \times 12 = 1728 \][/tex]
Comparison:
[tex]\[ 1728 \neq 36 \][/tex]
This expression is not correct.
b.) [tex]\( 5^2 = 25 \)[/tex]
Calculate [tex]\( 5^2 \)[/tex]:
[tex]\[ 5^2 = 5 \times 5 = 25 \][/tex]
Comparison:
[tex]\[ 25 = 25 \][/tex]
This expression is correct.
c.) [tex]\( (-3)^3 = 27 \)[/tex]
Calculate [tex]\( (-3)^3 \)[/tex]:
[tex]\[ (-3)^3 = (-3) \times (-3) \times (-3) = -27 \][/tex]
Comparison:
[tex]\[ -27 \neq 27 \][/tex]
This expression is not correct.
d.) [tex]\( 6^2 = 12 \)[/tex]
Calculate [tex]\( 6^2 \)[/tex]:
[tex]\[ 6^2 = 6 \times 6 = 36 \][/tex]
Comparison:
[tex]\[ 36 \neq 12 \][/tex]
This expression is not correct.
Therefore, the correctly evaluated expression is:
[tex]\[ \boxed{b.) \, 5^2 = 25} \][/tex]
