Question

Convert each of the following expression. Solve part C only

Answer 1

Solution:

Given;

$(-36)^{\frac{1}{2}}$

We would apply indices law where;

$(ab)^c=a^c\times b^c$

Thus;

$\begin{gathered} (-36)^{\frac{1}{2}}=(-1\times36)^{\frac{1}{2}} \\ (-1\times36)^{\frac{1}{2}}=(-1)^{\frac{1}{2}}\times(6^2)^{\frac{1}{2}} \\ \end{gathered}$

We would apply the power law of indices;

$(a^b)^c=a^{b\times c}=a^{bc}$

Then, we have;

$\begin{gathered} (-1\times36)^{\frac{1}{2}}=i\times6^{} \\ (-1\times36)^{\frac{1}{2}}=6i \\ (-36)^{\frac{1}{2}}=6i \\ \text{Where;} \\ i\text{ is a complex number} \end{gathered}$

FINAL ANSWER:

$\text{None}$