1. ## Exponents & Radicals Problems

I am 13 years old. I would like to solve more & more problems related to the topic exponents & radicals like the ones given in the URLs 1. Integral Exponents (Example 4, Exercises Question 2 & 3) & 2. Fractional Exponents (Example 3). I have been searching the net to get such problems but am not able to find such problems (the problems I have come across are far too easy).

Can someone please suggest me some websites wherein I can find such problems on exponents & radicals?

Thanks,

Ron

2. Originally Posted by rn5a
I am 13 years old. I would like to solve more & more problems related to the topic exponents & radicals like the ones given in the URLs 1. Integral Exponents (Example 4, Exercises Question 2 & 3) & 2. Fractional Exponents (Example 3). I have been searching the net to get such problems but am not able to find such problems (the problems I have come across are far too easy).

Can someone please suggest me some websites wherein I can find such problems on exponents & radicals?

Thanks,

Ron

Google search "Exponents Worksheets" and "Surds Worksheets" or just buy a year 10 text book. Second hand texts go for about \$5 where i'm from.

3. I am not sure about websites, but my old Saxon algebra textbooks have a ton of these kinds of problems. I can give you a few of the harder ones:

1. $(x^3y)^{-2}(xy^3)^{-4}$

2. $\frac{a^{x/2}(y^{2-x})^{1/2}}{a^{3x}y^{-2x}}$

3. $x^{3/4}\sqrt{xy}x^{1/2}\sqrt[3]{x^4}$

4. $\frac{y^{x+3}y^{x/2-1}z^a}{y^{(x-a)/2}z^{(x-a)/3}}$

5. $\sqrt{x^3y^2}\sqrt[4]{xy^3}$

Is that what you've looking for? I have the answers to these, and more problems, if you need them.

4. Originally Posted by Ragnarok
I am not sure about websites, but my old Saxon algebra textbooks have a ton of these kinds of problems. I can give you a few of the harder ones:

1. $(x^3y)^{-2}(xy^3)^{-4}$

2. $\frac{a^{x/2}(y^{2-x})^{1/2}}{a^{3x}y^{-2x}}$

3. $x^{3/4}\sqrt{xy}x^{1/2}\sqrt[3]{x^4}$

4. $\frac{y^{x+3}y^{x/2-1}z^a}{y^{(x-a)/2}z^{(x-a)/3}}$

5. $\sqrt{x^3y^2}\sqrt[4]{xy^3}$

Is that what you've looking for? I have the answers to these, and more problems, if you need them.
Thanks, mate...that's exactly what I am looking out for. Can you please give me many more such problems along with the answers (as many as you can....the more the better)? It would be great if you could do that.

5. No problem. I'm away from my books right now so I'll have to get back to you in a little while for the extra problems, but here are my answers to the ones I already gave you (if you need explanations I can give them):

1. $x^{-10}y^{-14}$
2. $a^{-5x/2}y^{1+3x/2}$
3. $x^{37/12}y^{1/2}$
4. $y^{(2x+4+a)/2}z^{(4a-x)/3}$
5. $x^{7/4}y^{7/4}$

The Saxon math textbooks are great, by the way, particularly for self-teaching. They have more practice than you'll ever need, as well.

6. Originally Posted by Ragnarok
No problem. I'm away from my books right now so I'll have to get back to you in a little while for the extra problems, but here are my answers to the ones I already gave you (if you need explanations I can give them):

1. $x^{-10}y^{-14}$
2. $a^{-5x/2}y^{1+3x/2}$
3. $x^{37/12}y^{1/2}$
4. $y^{(2x+4+a)/2}z^{(4a-x)/3}$
5. $x^{7/4}y^{7/4}$

The Saxon math textbooks are great, by the way, particularly for self-teaching. They have more practice than you'll ever need, as well.
Thank you so much, my dear friend, for your inputs. I will wait for the other problems.

Ron

7. You need this book - Elementary Algebra for Schools by Hall and Knight. You can read it online, if you click on it, as well as print (where necessary). There is a chapter called Elementary Surds (click to jump there) and it will provide more than enough examples and exercises for your purposes. If you finish with that (by which time you know a great deal already), there is an advanced version called Higher Algebra, which is also available for free (click to view it).

8. Funny, TheCoffeeMachine, I have never heard the term "surds" in my life. Is it maybe a British/Australian term or is this just my years of skipping school catching up to me?

Some more problems:

1. $\sqrt{x^3y}\sqrt[4]{xy^3}$

2. $(\sqrt{3}+\sqrt{x})^2$

3. $\frac{x^{-2}+y^{-2}}{(xy)^{-1}}$

4. $(\sqrt{2}-\sqrt{x})(1-\sqrt{x})$

5. $y^{x/2+1}\sqrt{y^a}2y^{2a+3}$

6. $\frac{a^{x/2}(y^{2-x})^{1/2}}{a^{4x}y^{-2x}}$

7. $2\sqrt{\frac{3}{2}}-3\sqrt{\frac{2}{3}}+2\sqrt{24}$

8. $2\sqrt{\frac{7}{3}}-\sqrt{\frac{3}{7}}-2\sqrt{84}$

9. $\sqrt{2x}(\sqrt{3x}+\sqrt{x})$

10. $\frac{a^{-2}+b^{-1}}{a^{-1}b}$

1. $x^{7/4}y^{7/4}$

2. $3+2\sqrt{3}\sqrt{x}+x$

3. $\frac{x^2+y^2}{xy}$

4. $\sqrt{2}-(1+\sqrt{2})\sqrt{x}+x$

5. $2y^{5a/2+x/2+4}$

6. $a^{-7x/2}y^{(1+3x)/2}$

7. $4\sqrt{6}$

8. $-\frac{73\sqrt{21}}{21}$

9. $x(\sqrt{6}+\sqrt{2})$

10. $\frac{b+a^2}{ab^2}$

Edit: Sorry, I think #1 is a repeat. Oh well, I don't feel like changing it.