1. ## how to multiply

i got this one and dont know how to solve it. i got problems with multiplying

1. 5^2/3 * 5^4/3 =

2. (8th root of 4^5) ^-8/5

2. $\displaystyle a^b \cdot a^c = a^{b+c}$

$\displaystyle a^n \cdot b^n = (a\cdot b)^n$

$\displaystyle (a^b)^c = a^{b\cdot c}$

3. Originally Posted by makaveli89
i got this one and dont know how to solve it. i got problems with multiplying

1. 5^2/3 * 5^4/3 =

2. (8th root of 4^5) ^-8/5
$\displaystyle 5^\frac{2}{3}\cdot5^\frac{4}{3}=5^\frac{6}{3}=5^2= \boxed{25}$

$\displaystyle \left[\left(4^5\right)^\frac{1}{8}\right]^{-\frac{8}{5}}=4^{-\frac{40}{40}}=4^{-1}=\boxed{\frac{1}{4}}$

4. Originally Posted by masters
$\displaystyle 5^\frac{2}{3}\cdot5^\frac{4}{3}=5^\frac{6}{3}=5^2= \boxed{25}$

$\displaystyle \left[\left(4^5\right)^\frac{1}{8}\right]^{-\frac{8}{5}}=4^{-\frac{40}{40}}=4^{-1}=\boxed{\frac{1}{4}}$
Masters, I know solving them too. But these are not trick questions, its only about knowing the rule and applying it. Apparently, makaveli89 doesn't know these basic rules. So why giving the answers instead of teaching?

5. Originally Posted by wingless
Masters, I know solving them too. But these are not trick questions, its only about knowing the rule and applying it. Apparently, makaveli89 doesn't know these basic rules. So why giving the answers instead of teaching?
Wingless,
Sometimes I stop short of finishing the exercises. Sometimes I finish to let the finished exercise serve as a model for subsequent similar exercises. If the questioner has only a couple of exercises, then I may make the assumption that he/she got through everything else, but was stumped on these two. So I expedited the lesson.

Other tutors like to just give hints. That's fine. Some posters get frustrated with just hints.

In my teaching, I have been successful doing both.

But, thanks for your comments. In the future I'll try to be more judicious in my responses.

6. i have a question.
why didn't you multiply 5 to 5.. ?

7. Originally Posted by crystallizedreverie
i have a question.
why didn't you multiply 5 to 5.. ?
If your question is about this $\displaystyle 5^\frac{2}{3}\cdot5^\frac{4}{3}=5^\frac{6}{3}=5^2= \boxed{25}$, it's because their exponents aren't same. The rule is $\displaystyle a^n \cdot b^n = (a\cdot b)^n$.

8. Answer to number one is 25
Answer to number two is 0.25