Full solution

Q. Simplify. Express your answer using positive exponents.

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\frac{10u}{2u^4}

Identify Expression Components: Write down the expression and identify the coefficients and the variables. $\newline$ The expression is $\frac{10u}{2u^4}$ . We have the coefficient $10$ in the numerator and $2$ in the denominator. The variable $u$ is in both the numerator and the denominator with an exponent of $1$ in the numerator and $4$ in the denominator.
Simplify Coefficients: Simplify the coefficients by dividing them. $\newline$ $\frac{10}{2} = 5$ . $\newline$ So, $\frac{10u}{2u^4}$ becomes $\frac{5u}{1u^4}$ .
Subtract Exponents: Simplify the variable part by subtracting the exponents. $\newline$ When dividing powers with the same base, subtract the exponents: $u^1/u^4 = u^{1-4} = u^{-3}$ . $\newline$ However, we need to express the answer using positive exponents.
Convert Negative Exponent: Convert the negative exponent to a positive exponent. $\newline$ To convert $u^{-3}$ to a positive exponent, we write it as $1/u^3$ . $\newline$ So, $5u/1u^4$ becomes $5/1u^3$ .
Remove Unnecessary Term: Simplify the expression by removing the $1$ . The expression $\frac{5}{1u^3}$ simplifies to $\frac{5}{u^3}$ .