How do you write $\sqrt{x^{5}}$ $sqrt (x^5)$ as an exponential form?

Question

49899 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-31T01:00:18

The square root is expressed as an exponent of $\frac{1}{2}$ $1/2$ , so $\sqrt{x^{5}}$ $sqrt(x^5)$ can be expressed as $x^{\frac{5}{2}}$ $x^(5/2)$ .

Roots are expressed as fractional exponents:

$\sqrt[2]{x} = x^{\frac{1}{2}}$ $root(2)x=x^(1/2)$
$\sqrt[3]{x} = x^{\frac{1}{3}}$ $root(3)x=x^(1/3)$

and so on.

This makes sense, because when we multiply we add exponents:

$\sqrt{x}$ $sqrt(x)$ x $\sqrt{x}$ $sqrt(x)$ = $x$ $x$

$x^{\frac{1}{2}}$ $x^(1/2)$ x $x^{\frac{1}{2}}$ $x^(1/2)$ = $x^{(\frac{1}{2} + \frac{1}{2})}$ $x^((1/2+1/2))$ = $x^{1}$ $x^1$ = $x$ $x$

When an exponent is raised to another exponent, the exponents are multiplied:

$\sqrt{x^{5}} = {(x^{5})}^{\frac{1}{2}} = x^{5 \cdot \frac{1}{2}} = x^{\frac{5}{2}}$ $sqrt(x^5)=(x^5)^(1/2) = x^(5*1/2) = x^(5/2)$

How do you write sqrt (x^5)√x5sqrt (x^5) as an exponential form?