Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{5u^{10}}{(5u^{-2})^{3}}\\)

Explanation:

Step1: Expand denominator via exponent rule

$(5u^{-2})^3 = 5^3 \cdot (u^{-2})^3 = 125u^{-6}$

Step2: Rewrite the original fraction

$\frac{5u^{10}}{125u^{-6}}$

Step3: Simplify constant terms

$\frac{5}{125} = \frac{1}{25}$

Step4: Simplify variable terms (exponent subtraction)

$u^{10 - (-6)} = u^{16}$

Step5: Combine simplified terms

$\frac{1}{25} \cdot u^{16}$

Answer:

$\frac{u^{16}}{25}$