ASAP (Medal+Fan) Can someone simplify this???????? Pic

Question

nptweezy · Answer

This needs to be simplified

mathstudent55 · Answer

You need to memorize these rules of exponents and learn how to use them:

$ (ab)^n = a^nb^n$

$ (a^m)^n = a^{mn} $

$a^ma^n = a^{ m + n } $

$ \dfrac{a^m}{a^n} = a^{m - n} $

skullpatrol · Answer

For this question you only need the second rule.

mathstudent55 · Answer

Actually, for this problem, you need the first and second rules, but you should know all of them because you'll have to do problems with the other rules too.

mathstudent55 · Answer

Use the first rule in the numerator and denominator:

$ \dfrac{( 3x^6)^2}{ (4y^4)^3} $

$ = \dfrac{ 3^2(x^6)^2}{ 4^3(y^4)^3} $

skullpatrol · Answer

Also the definition of a power is helpful. $$b^n=b*b*...*b$$ n factors. The base is b and the exponent is n.

nptweezy · Answer

@skullpatrol do you know the answer

mathstudent55 · Answer

Now use the second rule:

$ = \dfrac{ 9x^{12}}{ 64y^{12}} $

skullpatrol · Answer

@NPTWEEZY yes, I do know the answer.