Question

What is 1/x∧-3/6 and how do you get to that answer?

Answer 1

Answer:

$x^\frac{1}{2}$

or

$\sqrt{x}$

Step-by-step explanation:

$\frac{1}{x^\frac{-3}{6}}$

I'm going to reduce -3/6 to -1/2 by dividing top and bottom of -3/6 by 3.

$\frac{1}{x^\frac{-1}{2}}$

Now I'm going to get rid of the negative exponent by moving x to the top; so -1/2 will change to 1/2 instead when doing this:

$1x^\frac{1}{2}$

$x^\frac{1}{2}$

$\sqrt{x}$

Please let know if I read the problem right:

$\frac{1}{x^\frac{-3}{6}}$

Answer 2

Answer:

The answer is  $\sqrt{x}$

Step-by-step explanation:

Step 1: Deal with the negative exponent applying this rule:

$x^{-b} = \frac{1}{x^{b}}$

In this case

$b=- \frac{3}{6}$

Putting all together:

$\frac{1}{x^{-\frac{3}{6}}} =x^{-(-\frac{3}{6}) } =x^{\frac{3}{6}}$

Step 2: Reduce the fractional exponent

The fractional exponent $\frac{3}{6}$ can be reduced dividing the numerator and denominator of the fraction by the least common multiple.

In order to find it, we have

$3=(3)*(1)\\6=(3)*(2)$

Therefore, the least common multiple is 3

Reducing the fraction:

$\frac{3}{6}=\frac{3\div3}{6\div3}=\frac{1}{2}$

Therefore:

$x^{\frac{3}{6}}=x^{\frac{1}{2}}$

Step 3: Deal with the fractional exponent

A fractional exponent can be expressed as a root, following this rule:

$x^{ \frac{a}{b}} = \sqrt[b]{x^{a}}$

In this case:

$a=1\\b=2$

As the index of the root is 2, this is a square root, therefore:

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