Expressions with powers and roots

1003118101

Level: 
C
Which of the following inequalities describes a correct relationship between the numbers \( a \), \( b \), \( c \) if \( a=4^{2^4} \), \( b=3^{4^3} \), \( c=2^{3^4} \)? (Hint: Barring parentheses, \( x^{y^z} \) is equivalent to \( x^{\left(y^z\right)} \).)
\( a < c < b \)
\( b < a < c \)
\( a < b < c \)
\( b < c < a \)

1003134510

Level: 
C
Complete the following sentence to obtain a true statement. The number \( \left( \sqrt3 \right)^{\sqrt2^{\sqrt[3]{64}}} \) is ...
a rational number less than \( 10 \).
an irrational number less than \( 10 \).
an integer greater than \( 10 \).
a rational number greater than \( 10 \).