Question

Use the associative property to simplify the expression 3x (x²) to its simplest equivalent form?

Answer 1

`\(3x(x^2)\) simplifies to \(3x^3\).`

Step-by-step explanation:

To simplify the expression
`\(3x(x^2)\)` using the associative property, we group the terms according to their common factors. In this case, the associative property allows us to associate the
`\(x\)` terms together. By doing so, we rewrite the expression as
`\(3 \cdot (x \cdot x^2)\)`.

Now, we can apply the product rule for exponents, which states that
`\(a^(m) \cdot a^(n) = a^(m+n)\)`. In our expression,
`\(x \cdot x^2\)`becomes
`\(x^(1+2) = x^3\).` Substituting this back into the grouped expression gives us
`\(3 \cdot x^3\)`, which is the simplest equivalent form of the original expression.

Therefore,
`\(3x(x^2)\)` simplifies to
`\(3x^3\)`. This process demonstrates the application of the associative property and the rules of exponents to efficiently simplify algebraic expressions.