Question

express the following fraction in simplest form, only using positive exponents.
$\frac{10k^{-10}b^{-9}}{5(k^{-5}b^{2})^{-3}}$

Explanation:

Step1: Simplify the coefficient

$\frac{10}{5}=2$

Step2: Simplify denominator's exponent term

$(k^{-5}b^2)^{-3}=k^{(-5)\times(-3)}b^{2\times(-3)}=k^{15}b^{-6}$

Step3: Subtract exponents for $k$

$k^{-10-15}=k^{-25}$

Step4: Subtract exponents for $b$

$b^{-9-(-6)}=b^{-3}$

Step5: Combine all simplified parts

$2\times k^{-25}\times b^{-3}$

Answer:

$2k^{-25}b^{-3}$