Question: Simplify. (\frac{y^2}{5x^4})^3 Write your answer without parentheses.

Simplify. (\frac{y^2}{5x^4})^3 Write your answer without parentheses.

Solution

To simplify the expression \(\left( \frac{y^2}{5x^4} \right)^3\), follow these steps: Apply the power of a quotient rule, which states \(\left( \frac{a}{b} \right)^n = \frac{a^n}{b^n}\): \[ \frac{(y^2)^3}{(5x^4)^3} \] Raise the numerator and denominator to the power of 3: \[ \frac{y^{2 \times 3}}{5^3 \cdot x^{4 \times 3}} \] Calculate the powers: \[ \frac{y^6}{125x^{12}} \] So the simplified expression is: \[ \frac{y^6}{125x^{12}} \]