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Write a numerical expression for the verbal expression: the cube of the quotient of 18 and 6, then find it's value.

what is the best answer for the first part $(18\div6)^{3}$ or $3^3$? and if the second choice is the best one can we call it a numerical expression?

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    IMHO the first one depicts better what the sentence means otherwise the statement would have simply been "the cube of 3". Note also that you maybe have mixed the exponents in your suggestions. – 2017-02-20
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    The first one is better answer. As question asks you to write numerical expression and not evaluate it. For $3^3$ you will need to evaluate the quotient which is not asked. – 2017-02-20
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    @AmeyDeshpande Thanks, can we call $3^3$ a numerical expression or is it just a number in the exponent form? – 2017-02-20
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    Depends on the context. If numerical expression is defined as something which involves at least one numerical operation, then $3^3 = 3 \times 3 \times 3$ should be called one. – 2017-02-20

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Let's remember the definition of a numerical expression: A numerical expression is an expression composed of only numbers and operational symbols. Both answers you have provided are not only equal to each other, but are both numerical expressions. However, the "best" answer for the question you were provided is $(18 \div 6)^3$, since that is representing what the question is. But, by the order of operations, it is equal to $3^3$. Bottom line: first answer is best, but both answers are numerical expressions.

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I would use your first answer, mostly because it's a literal transcription of the words to symbols. As a side note, you're welcome to use $\div$, but as far as I can tell it is not used anywhere except grade school, at least in the US. For all I know, you are in grade school, in which case it's completely appropriate.