Simplify. Write the expression using only positive exponents.$\frac{8x^3}{2x^9}$8x32x9​​The simplified expression is .

Sure, let's simplify the given expression step by step.

Given expression: $\frac{8x^3}{2x^9}$

Step 1: Simplify the coefficients (numerical part). $\frac{8}{2} = 4$

Step 2: Simplify the exponents of $x$ using the quotient rule for exponents, which states $\frac{a^m}{a^n} = a^{m-n}$. $\frac{x^3}{x^9} = x^{3-9} = x^{-6}$

Step 3: Combine the simplified coefficient and the simplified exponent. $4x^{-6}$

Step 4: Write the expression using only positive exponents. Recall that $a^{-n} = \frac{1}{a^n}$. $4x^{-6} = 4 \cdot \frac{1}{x^6} = \frac{4}{x^6}$

Therefore, the simplified expression is $\frac{4}{x^6}$.