Chapter 7.1, Problem 66HP

To determine

To write: Three different expressions that can be simplified to $x^6$ .

Answer to Problem 66HP

The require three expressions that can be simplified to $x^6$ are:

  $x^2\left(x^4\right)$

  ${\left(x^3\right)}^2$

  $x^3\left(x^3\right)$

Explanation of Solution

Given information:

The expression $x^6$ .

Calculation:

Let the first expression be $x^2\left(x^4\right)$

  $x^2\left(x^4\right)$

  $=x^{2+4}$

(Product of powers)

  $=x^6$

(Simplify)

Hence ok.

Let the second expression be ${\left(x^3\right)}^2$

  ${\left(x^3\right)}^2$

  $=x^{3\cdot 2}$

(Power of a power)

  $=x^6$

(Simplify)

Hence ok.

Let the third expression be $x^3\left(x^3\right)$

  $x^3\left(x^3\right)$

  $=x^{3+3}$

(Product of powers)

  $=x^6$

(Simlify)

Hence ok.

Therefore, the three expressions are:

  $x^2\left(x^4\right)$

  ${\left(x^3\right)}^2$

  $x^3\left(x^3\right)$