Question

question
fully simplify using only positive exponents.
\\(\frac{125x^{2}y^{3}}{5xy^{7}}\\)
answer attempt 1 out of 2
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Explanation:

Step1: Simplify the coefficient

Divide 125 by 5.
$\frac{125}{5} = 25$

Step2: Simplify the x - terms

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

Step3: Simplify the y - terms

Using the rule $\frac{a^m}{a^n}=a^{m - n}$, for $y$ terms: $\frac{y^{3}}{y^{7}}=y^{3 - 7}=y^{- 4}$. Since we need positive exponents, $y^{-4}=\frac{1}{y^{4}}$

Step4: Combine the results

Multiply the simplified coefficient, x - term, and y - term together: $25\times x\times\frac{1}{y^{4}}=\frac{25x}{y^{4}}$

Answer:

$\frac{25x}{y^{4}}$