Chapter SH, Problem 6.12EP

To determine

Find the simplified form of the given expression.

Answer to Problem 6.12EP

The simplified form of the expression is $7x^2{y}^3$ .

Explanation of Solution

Given:

The given expression is $\sqrt[3]{343x^6{y}^9}$ .

Calculation:

  $\sqrt[3]{343x^6{y}^9}$

Use exponent rule $x^{pq}={\left(x^p\right)}^q$ .

  $\begin{array}{l}\sqrt[3]{343x^6{y}^9}\\ =\sqrt[3]{7^3{\left(x^2\right)}^3{\left(y^3\right)}^3}\\ =\sqrt[3]{7^3}\sqrt[3]{{\left(x^2\right)}^3}\sqrt[3]{{\left(y^3\right)}^3}\end{array}$

Apply radical property $\sqrt[n]{x^n}=x,x\ge 0$ .

  $=7x^2{y}^3$

Hence the simplified form of the expression is $7x^2{y}^3$ .