Chapter 7.3, Problem 24PPE

To determine

To simplify: The expression ${\left(5y^{\frac{1}{2}}\right)}^4$ .

Answer to Problem 24PPE

The required answer is $625y^2$ .

Explanation of Solution

Given information:

The given expression ${\left(5y^{\frac{1}{2}}\right)}^4$ .

Calculation:

  $\begin{array}{l}={\left(5y^{\frac{1}{2}}\right)}^4\\ =5^4{\left(y^{\frac{1}{2}}\right)}^4\end{array}$

(Raise each factor to the second power)

  $\begin{array}{l}=5^4{y}^{\frac{1}{2}\cdot 4}\\ =5^4{y}^2\end{array}$

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

  $=625y^2$

(Simplify)