Question

which one doesnt belong? there is no correct answer. it is all about your reasoning behind your choice. 4.78 x 7.5 $\frac{3}{2}$ x $\frac{1}{24}$ -6² (-6)²

Explanation:

Step1: Analyze the first expression

$4.78\times7.5$ is a multiplication of two non - integer decimal numbers.

Step2: Analyze the second expression

$\frac{3}{2}\times\frac{1}{24}=\frac{3\times1}{2\times24}=\frac{3}{48}=\frac{1}{16}$, it is a multiplication of two fractions.

Step3: Analyze the third expression

$-6^{2}=- (6\times6)= - 36$, here the exponentiation is applied only to 6 and then the negative sign is applied.

Step4: Analyze the fourth expression

$(-6)^{2}=(-6)\times(-6) = 36$, here the negative 6 is squared.
The first two are multiplications of non - negative numbers, while the third and fourth involve exponentiation. The third one $-6^{2}$ is different from the others in terms of the order of operations (negative sign not part of the base for exponentiation) compared to $(-6)^{2}$, and also different from the multiplication of non - integer decimals and fractions.

Answer:

$-6^{2}$