Question

simplify. express your answer using positive exponents. \\(\frac{10k^{-1}}{2k^{-1}}\\)

Explanation:

Step1: Simplify the coefficients

Divide the coefficient of the numerator (10) by the coefficient of the denominator (2). So, $\frac{10}{2} = 5$.

Step2: Simplify the variable terms

For the variable $k$ with exponents, use the quotient rule for exponents: $\frac{a^m}{a^n}=a^{m - n}$. Here, $m=-1$ and $n = - 1$, so $k^{-1-(-1)}=k^{-1 + 1}=k^{0}$. And we know that $a^{0}=1$ for $a
eq0$. So $k^{0}=1$.

Step3: Multiply the results from Step1 and Step2

Multiply 5 (from Step1) and 1 (from Step2), we get $5\times1 = 5$.

Answer:

5