Chapter 3.1, Problem 4QR

Solution

To Find: The value of $4^{\frac{5}{2}}$

  $4^{\frac{5}{2}}=32$

Given information:

  $4^{\frac{5}{2}}$

Concept and Formula Used:

We use the concept of finding $n^{th}$ root. $\sqrt[n]{a}={(a)}^{\frac{1}{n}}$ and ${(a^m)}^n={(a)}^{m\times n}$

Calculation:

It is given that $4^{\frac{5}{2}}$

Write $4^{\frac{5}{2}}$ in factor form and simplify using ${(a^m)}^n={(a)}^{m\times n}$

  $\begin{array}{l}$ 4^{\frac{5}{2}}={(2\times 2)}^{\frac{5}{2}}$$ 4^{\frac{5}{2}}={\left({(2)}^2\right)}^{\frac{5}{2}}$$ 4^{\frac{5}{2}}={(2)}^{2\times \frac{5}{2}}$$ 4^{\frac{5}{2}}={(2)}^5$4^{\frac{5}{2}}=32\end{array}$

Conclusion:

  $4^{\frac{5}{2}}=32$