Question

simplify the expression. write the answer with assume all variables represent nonzero real num\\(\left(\frac{5x^{3}}{3y^{2}}\
ight)^{-2}=\square\\)

Explanation:

Step1: Apply the negative exponent rule

Recall that \((\frac{a}{b})^{-n}=(\frac{b}{a})^{n}\). So, \((\frac{5x^{3}}{3y^{2}})^{-2}=(\frac{3y^{2}}{5x^{3}})^{2}\)

Step2: Apply the power of a quotient rule

The power of a quotient rule states that \((\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}\). So, \((\frac{3y^{2}}{5x^{3}})^{2}=\frac{(3y^{2})^{2}}{(5x^{3})^{2}}\)

Step3: Apply the power of a product rule

The power of a product rule states that \((ab)^{n}=a^{n}b^{n}\). So, \(\frac{(3y^{2})^{2}}{(5x^{3})^{2}}=\frac{3^{2}(y^{2})^{2}}{5^{2}(x^{3})^{2}}\)

Step4: Simplify the exponents

Recall that \((a^{m})^{n}=a^{mn}\). So, \(\frac{3^{2}(y^{2})^{2}}{5^{2}(x^{3})^{2}}=\frac{9y^{4}}{25x^{6}}\)

Answer:

\(\frac{9y^{4}}{25x^{6}}\)