Chapter 7.3, Problem 3LC

To determine

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

Answer to Problem 3LC

The required answer is $b^{-21}$ .

Explanation of Solution

Given information:

The given expression ${\left(3a^{\frac{1}{2}}\right)}^4$ .

Calculation:

  $\begin{array}{l}={\left(3a^{\frac{1}{2}}\right)}^4\\ =3^4{\left(a^{\frac{1}{2}}\right)}^4\end{array}$

(Raise each factor to the second power)

  $=3^4{a}^{\frac{1}{2}\cdot 4}$

(Multiply the exponents of a power raised to a power)

  $=81a^2$

(Simplify)