Express each power as a radical.

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September 5th 2012, 03:37 PM
ford2008

Express each power as a radical.

Hi guys,

the task: Express each power as a radical.

1. 9^1/2
my anser:

= root of 9

2. m^-1/2
my answer:

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

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

3. 3k^2/5
my answer:

= 5 root of 3k^2

4. ((pq^3)^4)^1/5
my answer:

= 5 root of pq^12

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

my answer:

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

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

Is that right? If not, please explain. Thanks.
September 5th 2012, 06:29 PM
topsquark

Re: Express each power as a radical.

Quote:

Originally Posted by ford2008

Hi guys,

the task: Express each power as a radical.

1. 9^1/2
my anser:

= root of 9

2. m^-1/2
my answer:

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

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

3. 3k^2/5
my answer:

= 5 root of 3k^2

4. ((pq^3)^4)^1/5
my answer:

= 5 root of pq^12

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

my answer:

= 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
September 6th 2012, 09:35 AM
ford2008

Re: Express each power as a radical.

Hey Dan,

thanks for your help.

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?

Thanks for your help.
September 6th 2012, 09:54 AM
Plato

Re: Express each power as a radical.

Quote:

Originally Posted by ford2008

3. 3k^2/5
my answer:

= 5 root of 3k^2

4. ((pq^3)^4)^1/5
my answer:

= 5 root of pq^12

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

$4 $.~~\sqrt[5]{p^4q^{12}}$
September 6th 2012, 11:27 AM
earboth

Re: Express each power as a radical.

Quote:

Originally Posted by ford2008

Hi guys,

the task: Express each power as a radical.

...
3. 3k^2/5
my answer:

= 5 root of 3k^2

4. ((pq^3)^4)^1/5
my answer:

= 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?

Thanks for your help.

According to your answer the 3 in your term doen't belong under the root-sign:

$3 \cdot k^{\frac25} = 3 \cdot \sqrt[5]{k^2}$

$\left ( \left (pq^3 \right )^4 \right )^{1/5} = p^\frac45 \cdot q^{\frac{12}5}$