Question

fully simplify using only positive exponents.\\(\frac{5xy}{5x^2y^8}\\)

Explanation:

Step1: Cancel common coefficients

The coefficient of numerator is 5 and denominator is 5, so $\frac{5}{5} = 1$.

Step2: Simplify x terms

Using the rule $\frac{x^m}{x^n}=x^{m - n}$, for $x$ terms: $\frac{x}{x^2}=x^{1 - 2}=x^{-1}=\frac{1}{x}$ (since $a^{-n}=\frac{1}{a^n}$).

Step3: Simplify y terms

Using the same exponent rule, for $y$ terms: $\frac{y}{y^8}=y^{1 - 8}=y^{-7}=\frac{1}{y^7}$.

Step4: Combine all simplified terms

Multiply the simplified coefficient, x term, and y term: $1\times\frac{1}{x}\times\frac{1}{y^7}=\frac{1}{x y^7}$.

Answer:

$\frac{1}{x y^7}$