Let's solve each part of the question step by step.
### Part (i): Expressing [tex]\(\sqrt{27}\)[/tex] in exponential form
The square root of a number can be represented in exponential form using the exponent [tex]\( \frac{1}{2} \)[/tex]. Thus,
[tex]\[
\sqrt{27} = 27^{\frac{1}{2}}
\][/tex]
The approximate value of this expression is:
[tex]\[
27^{\frac{1}{2}} \approx 5.196
\][/tex]
### Part (ii): Expressing [tex]\(\sqrt[4]{156}\)[/tex] in exponential form
The fourth root of a number can be represented in exponential form using the exponent [tex]\( \frac{1}{4} \)[/tex]. Thus,
[tex]\[
\sqrt[4]{156} = 156^{\frac{1}{4}}
\][/tex]
The approximate value of this expression is:
[tex]\[
156^{\frac{1}{4}} \approx 3.534
\][/tex]
### Summary
1. [tex]\(\sqrt{27} = 27^{\frac{1}{2}} \approx 5.196\)[/tex]
2. [tex]\(\sqrt[4]{156} = 156^{\frac{1}{4}} \approx 3.534\)[/tex]
By expressing the square root and fourth root in exponential form and approximating their values, we obtain:
[tex]\[
27^{\frac{1}{2}} \approx 5.196
\][/tex]
[tex]\[
156^{\frac{1}{4}} \approx 3.534
\][/tex]
These are the exponential forms and their corresponding approximate numerical values.
