Full solution

Q. Simplify. Express your answer using positive exponents.

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\frac{7n}{7n^2}

Write Expression: Write down the given expression. $\newline$ The given expression is $\frac{7n}{7n^2}$ . We need to simplify this expression.
Divide Numerator and Denominator: Simplify the expression by dividing the numerator by the denominator. $\newline$ Since both the numerator and the denominator have the common factor $7n$ , we can divide both by $7n$ to simplify the expression. $\newline$ $\frac{7n}{7n^2} = \left(\frac{7}{7}\right) \cdot \left(\frac{n}{n^2}\right)$
Simplify Coefficients and Variables: Simplify the coefficients and the variables separately. $\newline$ $\frac{7}{7} = 1$ (since any number divided by itself is $1$ ) $\newline$ $\frac{n}{n^2} = n^{1-2}$ (since when we divide powers with the same base, we subtract the exponents)
Write Simplified Form: Write down the simplified form of the expression. $\newline$ $1 \times n^{(1-2)} = n^{-1}$ $\newline$ However, the question prompt asks for positive exponents, so we need to express $n^{-1}$ as a positive exponent.
Express Negative Exponent: Express $n^{-1}$ with a positive exponent. $\newline$ $n^{-1}$ is the same as $\frac{1}{n^{1}}$ , which has a positive exponent.