Question

(1/10)^15 * (1/1000)^-6

Answer 1

   
[tex]\displaystyle\\ \left(\frac{1}{10}\right)^{15}\times\left(\frac{1}{1000}\right)^{-6}=\\\\\\ =\left(\frac{1}{10}\right)^{15}\times\left(\frac{1}{10^3}\right)^{-6}=\\\\\\ =\left(\frac{1}{10}\right)^{15}\times\left[\left(\frac{1}{10}\right)^3\right]^{-6}= \\\\\\ =\left(\frac{1}{10}\right)^{15}\times\left(\frac{1}{10} \right)^{3\times(-6)}=\\\\\\ =\left(\frac{1}{10}\right)^{15}\times\left(\frac{1}{10}\right)^{-18}=\\\\\\ =\left(\frac{1}{10}\right)^{15+(-18)}=\left(\frac{1}{10}\right)^{-3}=\boxed{10^3} [/tex]