Simplify expression with exponents

[ahmedb]

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

 

[Also sprach Zarathustra]

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]

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]

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} $

 

[CellCoree]

To simplify this expression, we can use the rules of exponents to rewrite the terms with negative exponents as fractions with positive exponents in the denominator. This will result in:

(((4x^6)^3(4/y^8))/((2x)^4(12/y^3)^2))^1/2

Next, we can use the power rule of exponents to simplify the terms inside the parentheses. This will result in:

(((64x^18)(4/y^8))/((16x^4)(144/y^6)))^1/2

We can then combine like terms in the numerator and denominator to get:

((256x^18)/(2304x^4y^14))^1/2

Next, we can use the quotient rule of exponents to simplify the fraction. This will result in:

(256/2304)(x^18/x^4)(y^-14)^1/2

Using the power rule of exponents again, we can simplify the terms inside the parentheses to get:

(1/9)(x^14)(1/y^7)

Finally, we can rewrite the expression with positive exponents to get the simplified form:

x^14/(9y^7)

Therefore, the simplified expression with positive exponents is x^14/(9y^7).