Question

Simplify [view attached image]

Answer 1

Given:

The given expression is $(\sqrt{5})( \sqrt[3]{5})$

We need to simplify the given expression.

Simplification:

Let us simplify the given expression.

Rewriting the given expression, we have;

$5^{\frac{1}{2}} \cdot 5^{\frac{1}{3}}$

Let us apply the exponent rule $\:a^b\cdot \:a^c=a^{b+c}$, we get;

$5^{\frac{1}{2}+\frac{1}{3}}$

Taking LCM, we have;

$5^{\frac{3+2}{6}}$

Simplifying, we get;

$5^{\frac{5}{6}}$

Thus, the simplified value of the given expression is $5^{\frac{5}{6}}$

Hence, Option a is the correct answer.