Full solution

Q. Simplify. Express your answer using positive exponents.

\newline

\frac{6m}{m^7}

Write Expression: Write down the given expression. $\newline$ The given expression is $\frac{6m}{m^7}$ . We need to simplify this expression by dividing the terms.
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ The quotient rule states that when you divide two powers with the same base, you subtract the exponents. In this case, the base is $m$ . $\newline$ $\frac{6m}{m^7} = 6 \times m^{1-7}$
Perform Subtraction: Perform the subtraction of the exponents. $\newline$ Subtract the exponents $1$ and $7$ . $\newline$ $m^{(1-7)} = m^{-6}$
Simplify Coefficient: Simplify the coefficient. $\newline$ The coefficient $6$ remains unchanged since it is not involved with the variable $m$ . $\newline$ $6 \times m^{-6}$
Express Negative Exponent: Express the negative exponent as a positive exponent. $\newline$ According to the rules of exponents, $m^{-6}$ can be written as $\frac{1}{m^6}$ . Therefore, we rewrite the expression with a positive exponent. $\newline$ $6 \times m^{-6} = \frac{6}{m^6}$
Combine Coefficient: Combine the coefficient and the positive exponent. The final simplified expression is: $\frac{6}{m^6}$