Simplify by expressing fractional exponents instead of radicals

Question

asked Nov 21, 2020 100k views

2 Answers

Eric Galluzzo · Answer 1 · 2020-11-26T05:02:34+0000

Answer:

$a^{(1)/(2)}b^{(1)/(2)}$

Explanation:

Given:

The expression in radical form is given as:

√(ab)

We need to express this in fractional exponent form.

We know that,

$\sqrt a=a^{(1)/(2)}$

Also,
$√(ab)=\sqrt a* \sqrt b$

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

$√(ab)=\sqrt a * \sqrt b\\\\√(ab)=a^{(1)/(2)}* b^{(1)/(2)}\\\\\therefore √(ab)=a^{(1)/(2)}b^{(1)/(2)}$

So, the given expression in fractional exponents form is
$a^{(1)/(2)}b^{(1)/(2)}$ .