$$\frac{(x ^{-5}x ^{4})^{4} }{ (x ^{4}x ^{-6})^{-5}}$$

Question

$$\frac{(x ^{-5}x ^{4})^{4}  }{ (x ^{4}x ^{-6})^{-5}}$$

anonymous · Answer

How do i do this...Yes it may be simple but for some reason i can't figure it out.

thesmartone · Answer

Hint:

First use this formula
$\sf(a^b)^c = a^{b\times c}$

Then use this one
$\sf\Large\frac{a^b}{a^c}=a^{b-c}$

anonymous · Answer

I know that

thesmartone · Answer

also these formulas:

$\sf a^b\times a^c = a^{b+c}$

$\sf\Large {a^{-b}}=\frac{1}{a^b}$

anonymous · Answer

yes i understand that...i just can't seem to get the correct answer to this...

phi · Answer

can you simplify $$ x ^{-5}x ^{4} $$?
(add the exponents)

anonymous · Answer

x^-1

phi · Answer

yes  now we have up top
$$ (x^{-1})^4 $$
now use the rule multiply exponents to simplify that

anonymous · Answer

X^-4

phi · Answer

now let's do the bottom. first
$$  (x ^{4}x ^{-6}) $$

anonymous · Answer

x^-2

phi · Answer

now (x^-2)^-5

anonymous · Answer

x^10

phi · Answer

so we have
$$ \frac{x^{-4}}{x^{10} }$$

anonymous · Answer

so 1/ x^14

phi · Answer

you can do that two ways:  "flip" x^-4  and put it in the bottom but with x^4
then combine x^4*x^10  (in the bottom)

or do -4 - 10  (subtract the exponents because we divide)

phi · Answer

yes 1/x^14  
this can also be written x^(-14)

anonymous · Answer

ok thank you!