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.

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

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

The other ones look good.

-Dan

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.

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

$4$\displaystyle .~~\sqrt[5]{p^4q^{12}}$

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:

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

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