Answer:
[tex]\frac{125}{27}[/tex]
Step-by-step explanation:
[tex]\frac{2^{-4} \times 15^{-3} \times 625}{5^2 \times 10^{-4}}[/tex]
Lets expand all the composite numbers into prime numbers.
[tex]=> \frac{2^{-4} \times (3^{-3} \times 5^{-3}) \times 5^4}{5^2 \times (2^{-4} \times 5^{-4})}[/tex]
Lets cancel [tex]2^{-4}[/tex] from numerator and denominator.
[tex]=> \frac{3^{-3} \times 5^{-3} \times 5^4}{5^2 \times 5^{-4}}[/tex]
Using laws of exponents , lets solve this.
[tex]=> \frac{3^{-3} \times 5^{(-3 + 4)}}{5^{( 2 - 4)}}[/tex]
[tex]=> \frac{3^{-3} \times 5^{1}}{5^{-2}}[/tex]
[tex]=> 3^{-3} \times 5^{[1 - (-2)]}[/tex]
[tex]=> 3^{-3} \times 5^{3}[/tex]
[tex]=> \frac{5^3}{3^3} = \frac{125}{27}[/tex]
