Question

Is the expression x^3 X x^3 X x^3 equivalent to x^3X3X3 ? Why or why not?

Answer 1

The given expressions are

$x^3\times x^3\times x^3\text{ and }x^{3\times3\times3}$

Consider the first expression

$x^3\times x^3\times x^3$$\text{Use the formula a}^n\times a^m\times a^p=a^{n+m+p},\text{ here a=x and n=3,m=3 and p=3}$

$x^3\times x^3\times x^3=x^{3+3+3}$

Adding 3,3 and 3, we get 9

$x^3\times x^3\times x^3=x^9$

Consider the second expression

$x^{3\times3\times3}$

Multiplying 3,3 and 3, we get 27

$x^{3\times3\times3}=x^{27}$

Equating both expressions as follows:

$x^3\times x^3\times x^3=x^{3\times3\times3}$

Substitute values, we get

$x^9=x^{27}$$\text{Use the conditions if a}^n=a^mimplies^{}_{}\text{ n=m, here a=x and n=9, m=27.}$$9=27$

It is not true.

Hence the given two expressions are not equivalent.

The reason is it doesn't satisfy the following condition

$x^n\times x^m_{}=x^{n+m}$