Question

Simplify by expressing fractional exponents instead of radicals

Answer 1

Answer:

$a^{\frac{1}{2}}b^{\frac{1}{2}}$

Step-by-step explanation:

Given:

The expression in radical form is given as:

$\sqrt{ab}$

We need to express this in fractional exponent form.

We know that,

$\sqrt a=a^{\frac{1}{2}}$

Also, $\sqrt{ab}=\sqrt a\times \sqrt b$

Now, clubbing both the properties of square root function, we can rewrite the given expression as:

$\sqrt{ab}=\sqrt a \times \sqrt b\\\\\sqrt{ab}=a^{\frac{1}{2}}\times b^{\frac{1}{2}}\\\\\therefore \sqrt{ab}=a^{\frac{1}{2}}b^{\frac{1}{2}}$

So, the given expression in fractional exponents form is $a^{\frac{1}{2}}b^{\frac{1}{2}}$.