Full solution

Q. Simplify. Express your answer using positive exponents.

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\frac{6n}{3n^8}

Identify Coefficients and Powers: Identify the coefficients and the powers of $n$ in the expression. $\newline$ The expression $\frac{6n}{3n^8}$ consists of the coefficient $6$ in the numerator and $3$ in the denominator, and the powers of $n$ are $n$ in the numerator and $n^8$ in the denominator.
Simplify Coefficients: Simplify the coefficients by dividing $6$ by $3$ . $\newline$ $6$ divided by $3$ equals $2$ . $\newline$ Calculation: $\frac{6}{3} = 2$
Apply Quotient Rule for Exponents: Apply the quotient rule for exponents to simplify $n/n^8$ . The quotient rule states that when dividing like bases, you subtract the exponents. Calculation: $n^1 / n^8 = n^{1-8} = n^{-7}$
Rewrite Negative Exponent: Since we want to express the answer using positive exponents, we rewrite $n^{-7}$ as $1/n^7$ . $\newline$ $n^{-7}$ is the same as $1/n^7$ because a negative exponent indicates the reciprocal of the base raised to the positive exponent.
Combine Results: Combine the results from steps $2$ and $4$ to write the final simplified expression. $\newline$ The final answer is $2 \times \frac{1}{n^7}$ , which simplifies to $\frac{2}{n^7}$ .