Question

Simplify the expression. The simplified expression should have no negative exponents. $$ \left(\frac{2 x^{3} y^{4}}{3 x y}\right)^{3} $$

Short answer

\[ \frac{8 x^{6} y^{9}}{27} \]

Step-by-step solution

Simplify the expression inside the parentheses

Firstly, you simplify the expression inside parentheses, by using the rule of exponent a^m / a^n = a^(m-n), therefore we get: \[ \left(\frac{2 x^{3-1} y^{4-1}}{3}\right)^{3} = \left(\frac{2 x^{2} y^{3}}{3}\right)^{3}\]

Apply power of a power rule

Apply the power of a power rule. This rule states that when a power is raised to a power, the exponents are multiplied. Then apply the power to each element inside the parentheses which gives us: \[ \left(\frac{2^{3} x^{2*3} y^{3*3}}{3^{3}} \right) = \frac{8 x^{6} y^{9}}{27} \]

Write final expression

The final expression has no negative exponents, and it is simplified. Therefore, the simplified expression is: \[ \frac{8 x^{6} y^{9}}{27} \]