How do I simplify these expressions in my maths test?

[Gringo123]

I got the following 2 questions in a recent maths test. Can anyone please explain the correct way to simplify these expressions?

4u to the power of 3 v to the power of 6 / 8u to the power of 2 v to the power of 3

3x to the power of 6 y to the power of 5 z to the power of 3 / 9x to the power of 4 y to the power of 2 z

I know that the answers are:
uv to the power of 3 / 2
and
x to the power of 2 y to the power of 3 z to the power of 2 / 3

... which were nothing like my answers!
Thanks

 

[tiny-tim]

Hi Gringo123!

erm … first write it out in maths instead of in English … that alone may help you!

(and use the X² tag just above the Reply box )

Then show us what you've done, so we'll know how to help!

 

[HallsofIvy]

I got the following 2 questions in a recent maths test. Can anyone please explain the correct way to simplify these expressions?

4u to the power of 3 v to the power of 6 / 8u to the power of 2 v to the power of 3

I think you mean
$$\frac{4u^3v^6}{8u^2v^3}= \frac{4}{8}\frac{u^3}{u^2}\frac{v^6}{v^3}$$

cancel in each fraction.

3x to the power of 6 y to the power of 5 z to the power of 3 / 9x to the power of 4 y to the power of 2 z

$$\frac{3x^6 y^5z^3}{9x^4y^2z}= \frac{3}{9}\frac{x^6}{x^2}\frac{y^5}{y^2}\frac{z^3}{z}$$

Again, cancel in each fraction.

I know that the answers are:
uv to the power of 3 / 2
and
x to the power of 2 y to the power of 3 z to the power of 2 / 3

... which were nothing like my answers!
Thanks

I've done those using "LaTex" but you can also get exponents with [ sup ] and [ /sup ] (without the spaces) x[ sup ]2[ /sup ] gives x². Or you can indicate exponents with ^: x^2. Oh, and please use parentheses so we can be sure you mean 4(u^3), not (4u^3).

 

[Mentallic]

Oh, and please use parentheses so we can be sure you mean 4(u^3), not (4u^3).

And while 4(u^3)=(4u^3) be sure to use parenthesis to indicate the power is only on u.
for e.g. 4u^3 is read as 4*u^3 while (4u)^3 is read as 4^3*u^3.

 

[Gringo123]

Thanks a lot for your help!