Question

simplify the following expression to simplest form using only positive exponents.\\((32x^{25}y^{-5})^{\frac{1}{5}}\\)

Explanation:

Step1: Apply power to each term

$$(32)^{\frac{1}{5}} \cdot (x^{25})^{\frac{1}{5}} \cdot (y^{-5})^{\frac{1}{5}}$$

Step2: Simplify constant term

$32=2^5$, so $(2^5)^{\frac{1}{5}}=2^{5 \cdot \frac{1}{5}}=2$

Step3: Simplify $x$ term

$$(x^{25})^{\frac{1}{5}}=x^{25 \cdot \frac{1}{5}}=x^5$$

Step4: Simplify $y$ term

$$(y^{-5})^{\frac{1}{5}}=y^{-5 \cdot \frac{1}{5}}=y^{-1}=\frac{1}{y}$$

Step5: Combine all simplified terms

$$2 \cdot x^5 \cdot \frac{1}{y}$$

Answer:

$\frac{2x^5}{y}$