Chapter 7.3, Problem 12P

Simplify each expression.

${\left(u^2\right)}^3{\left(w^4\right)}^{\frac{1}{3}}$

To determine

To simplify: The expression ${\left(v^2\right)}^3{\left(w^4\right)}^{\frac{1}{3}}$ .

Answer to Problem 12P

  $v^6{w}^{\frac{4}{3}}$

Explanation of Solution

Given information:

The expression is ${\left(v^2\right)}^3{\left(w^4\right)}^{\frac{1}{3}}$ .

Calculation:

Use multiplication property of exponents which is ${\left(x^a\right)}^b=x^{ab}$ .

  $\begin{array}{c}{\left(v^2\right)}^3{\left(w^4\right)}^{\frac{1}{3}}=\left(v^{2\times 3}\right)\left(w^{4\times \frac{1}{3}}\right)\\ =v^6{w}^{\frac{4}{3}}\end{array}$