Question

Write three different expressions that can be simplified to$x^6$.

Short answer

The three different expressions that can be simplified as $x^6$are

$x^2\times x^4,x^3\times x^3,\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}x\times x^5$

Step-by-step solution

Step 1. State the multiplication rule of laws of indices.

If the two terms have the same base (in this case x) and are to be multiplied together their indices are added.

In general:$x^m\times x^n=x^{m+n}$

Step 2. Find the three different additions in which number 6 will be obtained.

The number 6 can be obtained in the following three different ways.

$\begin{array}{l}2+4=6\\ 3+3=6\\ 1+5=6\end{array}$

Step 3. Find the required expression.

Using the multiplication rule of indices the three different expression that can be simplified to $x^6$are as follows.

$$\begin{gathered} x^6=x^{2+4} \\ =x^2\times x^4 \\ {x}^6=x^{3+3} \\ =x^3\times x^{30} \\ {x}^6=x^{1+5} \\ =x^1\times x^5 \\ =x\times x^5\left[x^1=x\right] \end{gathered}$$

Therefore, the required expression are$x^2\times x^4,x^3\times x^3\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}x}\times x^5.$