A coefficient (a) and an exponent (b) are missing in the two monomials shown below.
\[
a x^{3}
\]
The least common multiple (LCM) of the two monomials is \( 18 x^{5} \). Which pair of statements about the missing coefficient and the missing exponent is true?
A. The missing coefficient (a) must be 9 or 18.
The missing exponent (b) must be 5 .
B. The missing coefficient (a) must be 9 or 18 .
The missing exponent (b) can be any number 5 or less.
C. The missing coefficient (a) can be any multiple of 3. The missing exponent (b) must be 5 .
D. The missing coefficient (a) can be any multiple of 3 . The missing exponent \( (b) \) can be any number 5 or less.
Answer
Determine the possible values of a and b: a = 9, 18, b = 5
Step 1 ：Find the LCM of coefficients and exponents: \(\operatorname{lcm}(a, 18) = 18\), \(\operatorname{lcm}(3, b) = 5\)
Step 2 ：Solve the equations: \(a \mid 18\), \(b \mid 5\)
Step 3 ：Determine the possible values of a and b: a = 9, 18, b = 5
