Is the expression x3•x3•x3 equivalent to x3•3•3? Why or why not? Explain your reasoning.
It is not because when numbers have an exponent and are multiplied, the exponents are added.
For example:
\(x^{3}\) × \(x^{3}\) × \(x^{3}\) = \(x^{9}\)
When a number with an exponent is multiplied with a whole number, the coefficients are multiplied. In this case \(x^{3}\) has an imaginary 1 being multiplied to it, so 1 will be multiplied to the other numbers.
\(1 x^{3}\) × 3 × 3 = \(9x^{3}\)
Therefore, the expressions are not the same because the second equation does not have other variables being multiplied to it.
No, the expression \(x^3 * x^3 * x^3\) is not equivalent to \(x^{3*3*3}\)
The expression is given as:
\(x^3 * x^3 * x^3\)
Apply the law of indices
\(x^{3 +3 +3}\)
This means that:
\(x^3 * x^3 * x^3\) is equivalent to \(x^{3 +3 +3}\), not \(x^{3*3*3}\)
Hence, the expression \(x^3 * x^3 * x^3\) is not equivalent to \(x^{3*3*3}\)
Read more about equivalent expressions at:
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