Question

Simplify the expression. Assume that all variables are positive.

Answer 1

\[\left( \frac{ 8x^9y^3 }{ 27x^2y ^{12} } \right)^{\frac{ 2 }{ 3 }}\]

Answer 2

Please help me do this the easy way :)

Answer 3

First, rewrite 27 and 8 as powers.
Then, divide the x's and divide the y's inside the parentheses.
Then, apply the exponent outside the parentheses to every factor inside the parentheses.

Answer 4

Let's now do this step by step.
What is 8 expressed as a power?

Answer 5

\[8^{\frac{ 2 }{ 3 }}\]
which is \[\sqrt[3]{8^{2}}\]
which is \[\sqrt[3]{64} \]

which is 4

Answer 6

You are doing too many steps at once.
8 is the same as 2^3
27 is the same as 3^3
That means you have now:
\(\large \left( \dfrac{ 2^3x^9y^3 }{ 3^3x^2y ^{12} } \right)^{\frac{ 2 }{ 3 }}\)

Answer 7

oh ok lol

Answer 8

Now let's divide the x's and the y's using the rules of exponents.
\(\large \left( \dfrac{ 2^3x^7 }{ 3^3y ^9 } \right)^{\frac{ 2 }{ 3 }}\)

Answer 9

Now we raise every factor to the 2/3 power:
\(\Large \dfrac{ (2^3)^{\frac{2}{3}}(x^7)^{\frac{2}{3}} }{ (3^3)^{\frac{2}{3}}(y ^9)^{\frac{2}{3}} } \)

Answer 10

To raise an exponent to an exponent, multiply the exponents.

\(\Large \dfrac{ (2^2)(x^{\frac{14}{3}}) }{ (3^2)(y ^6) } \)

Answer 11

\(\Large \dfrac{ 4\sqrt[3]{x^{14}} }{ 9y ^6 } \)

Answer 12

Did you follow the steps?

Answer 13

thank you so much now i understand :)

Answer 14

yeah i followed them one by one

Answer 15

Great!
You're welcome.