Given:
The given expression is [tex](\sqrt{5})( \sqrt[3]{5})[/tex]
We need to simplify the given expression.
Simplification:
Let us simplify the given expression.
Rewriting the given expression, we have;
[tex]5^{\frac{1}{2}} \cdot 5^{\frac{1}{3}}[/tex]
Let us apply the exponent rule [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex], we get;
[tex]5^{\frac{1}{2}+\frac{1}{3}}[/tex]
Taking LCM, we have;
[tex]5^{\frac{3+2}{6}}[/tex]
Simplifying, we get;
[tex]5^{\frac{5}{6}}[/tex]
Thus, the simplified value of the given expression is [tex]5^{\frac{5}{6}}[/tex]
Hence, Option a is the correct answer.
