What is the simplified form of 3 over x squared all over 1 over x-cubed ? x over 3 1 over 3x 3x 3 over x?

In order to understand and deduce what operation to use in this problem, I should rewrite the equation in an algebraic expression:

3/x² ÷ 1/x³

In dividing fractions, the step is to get the reciprocal of the divisor, then multiply it with the dividend. In this case, to get the reciprocal of the divisor, interchange the numerator and denominator of 1/x³. So, it becomes x³/1 or x³. The operation becomes

3/x² × x³ = 3x³/x²

Following the laws of exponents, when you divide variables, just find the difference of their exponents. Therefore,

3x³/x² = 3x³⁻² = 3x

The simplified answer is 3x.

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