simplify expression with exponents

MoneyKing

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

Also sprach Zarathustra

Member
Re: simplify

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

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

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

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

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

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

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

$$(\frac{x}{9y})^{7}$$

battleman13

New member
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
Hello, MoneyKing!

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

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

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