# Express each power as a radical.

• Sep 5th 2012, 03:37 PM
ford2008
Express each power as a radical.
Hi guys,

1. 9^1/2
my anser:

= root of 9

2. m^-1/2

= 1
------
m^1/2

= 1
--------
root of m

3. 3k^2/5

= 5 root of 3k^2

4. ((pq^3)^4)^1/5

= 5 root of pq^12

5. x^2/3 y^1/4
-------------
x^1/2 y^1/2

= x^4/6-3/6 y^1/4-2/4

= x^1/6 y^-1/4

Is that right? If not, please explain. Thanks.
• Sep 5th 2012, 06:29 PM
topsquark
Re: Express each power as a radical.
Quote:

Originally Posted by ford2008
Hi guys,

1. 9^1/2
my anser:

= root of 9

2. m^-1/2

= 1
------
m^1/2

= 1
--------
root of m

3. 3k^2/5

= 5 root of 3k^2

4. ((pq^3)^4)^1/5

= 5 root of pq^12

5. x^2/3 y^1/4
-------------
x^1/2 y^1/2

= x^4/6-3/6 y^1/4-2/4

= x^1/6 y^-1/4

Is that right? If not, please explain. Thanks.

Your notation on 3 and 4 are possibly wrong.

3. Is this $3k^{2/5}$ or $(3k)^{2/5}$ If it is the second one then you are correct.

4. Is this $\left ( \left (pq^3 \right )^4 \right )^{1/5}$ or $\left ( \left ( \left ( pq \right )^3 \right )^4 \right )^{1/5}$

The other ones look good.

-Dan
• Sep 6th 2012, 09:35 AM
ford2008
Re: Express each power as a radical.
Hey Dan,

No. 3. is the first one, so then I am wrong. But what is wrong then in my answer?

No. 4. is the first one. So is my answer right or not, if it is the first one?

• Sep 6th 2012, 09:54 AM
Plato
Re: Express each power as a radical.
Quote:

Originally Posted by ford2008
3. 3k^2/5

= 5 root of 3k^2

4. ((pq^3)^4)^1/5

= 5 root of pq^12

#3 $.~~\sqrt[5]{3k^2}$ NOT $5\sqrt{3k^2}$

\$4 $.~~\sqrt[5]{p^4q^{12}}$
• Sep 6th 2012, 11:27 AM
earboth
Re: Express each power as a radical.
Quote:

Originally Posted by ford2008
Hi guys,

...
3. 3k^2/5

= 5 root of 3k^2

4. ((pq^3)^4)^1/5

= 5 root of pq^12

...

Quote:

Originally Posted by ford2008
...

No. 3. is the first one, so then I am wrong. But what is wrong then in my answer?

No. 4. is the first one. So is my answer right or not, if it is the first one?

$3 \cdot k^{\frac25} = 3 \cdot \sqrt[5]{k^2}$
$\left ( \left (pq^3 \right )^4 \right )^{1/5} = p^\frac45 \cdot q^{\frac{12}5}$