Full solution

Q. Simplify. Express your answer using positive exponents.

\newline

\frac{10z}{5z^8}

Write Expression: Write down the given expression. $\newline$ The given expression is $\frac{10z}{5z^8}$ . We need to simplify this expression by dividing the coefficients and subtracting the exponents of like bases.
Divide Coefficients: Divide the coefficients. $\newline$ Divide $10$ by $5$ to get the coefficient for the simplified expression. $\newline$ $10 / 5 = 2$
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $z^1 / z^8 = z^{(1-8)} = z^{-7}$
Combine Results: Combine the results from Step $2$ and Step $3$ . Combine the coefficient from Step $2$ with the result from Step $3$ to get the final simplified expression. $2 * z^{-7}$ However, the question prompt asks for positive exponents, so we need to express $z^{-7}$ with a positive exponent.
Express with Positive Exponent: Express $z^{-7}$ with a positive exponent. $\newline$ To express $z^{-7}$ with a positive exponent, we write it as $1/z^7$ . $\newline$ Therefore, the final simplified expression is: $\newline$ $2 \times (1/z^7)$ or $2/z^7$