Question

simplify. express your answer using positive exponents.\\(\frac{(10k)(5k^{-1})}{5k^{-4}}\\)

Explanation:

Step1: Multiply numerator constants/variables

Multiply the constants and add exponents of $k$ in the numerator:
$(10k)(5k^{-1}) = 10\times5 \times k^{1+(-1)} = 50k^{0}$
Since $k^0=1$, this simplifies to $50$.
Now the expression is $\frac{50}{5k^{-4}}$

Step2: Simplify constants and exponents

Divide the constants, and rewrite the negative exponent as positive by moving $k^{-4}$ to the numerator:
$\frac{50}{5} \times k^{4} = 10k^{4}$

Answer:

$10k^4$