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simplify expression with exponents

MoneyKing

New member
Jan 31, 2012
4
simplify and answer should be in positive exponents.
(((4x^6)^3(4y^-8))/((2x)^4(12y^3)^2))^1/2
please help and thanks
 
Jan 31, 2012
54
Re: simplify

simplify and answer should be in positive exponents.
(((4x^6)^3(4y^-8))/((2x)^4(12y^3)^2))^1/2
please help and thanks

$$ \huge{(}\frac{{(4x^6)^3}4y^{-8}}{(2x)^4(12y^3)^2}\huge{)}^{\frac{1}{2}} $$

$$ \huge{(}\frac{{(4^3x^{18})}4y^{-8}}{(2^4x^4)(12^2y^6)}\huge{)}^{\frac{1}{2}} $$

$$ \huge{(}\frac{{(64x^{18})}4y^{-8}}{(16x^4)(144y^6)}\huge{)}^{\frac{1}{2}} $$

$$ \huge{(}\frac{4x^{14}}{36y^{14}}\huge{)}^{\frac{1}{2}} $$

$$ \huge{(}\frac{x^{14}}{9y^{14}}\huge{)}^{\frac{1}{2}} $$

$$ \huge{(}(\frac{x}{9y})^{14}\huge{)}^{\frac{1}{2}} $$

$$ (\frac{x}{9y})^{7} $$
 

battleman13

New member
Jan 31, 2012
6
Re: simplify

You should probably show any work you have tried first so that more importantly we can fix any misconceptions you may have about this process.

If your going any further in math the ability to do the work in this problem will be required.

You may now have the answer, but what you really need is the ability to reach it on your own.
 

soroban

Well-known member
Feb 2, 2012
409
Hello, MoneyKing!

$\text{Simplify: }\:\left[\dfrac{(4x^6)^3(4y^{-8})}{(2x)^4(12y^3)^2}\right]^{\frac{1}{2}}$

$\left[\dfrac{(4x^6)^3(4y^{-8})}{(2x)^4(12y^3)^2}\right]^{\frac{1}{2}} \;=\;\;\left[\dfrac{4^3(x^6)^3\cdot 4y^{-8}}{2^4x^4\cdot 12^2(y^3)^2}\right]^{\frac{1}{2}} \;=\;\;\left[\dfrac{64x^{18}\cdot 4y^{-8}}{16x^4\cdot144y^6}\right]^{\frac{1}{2}} $

. . . . . $=\;\;\left[\dfrac{x^{14}}{9y^{14}}\right]^{\frac{1}{2}} \;=\;\;
\dfrac{(x^{14})^{\frac{1}{2}}}{9^{\frac{1}{2}}(y^{14})^{\frac{1}{2}}} \;=\;\;\dfrac{x^7}{3y^7} $