Final answer:
To simplify the expression, divide the exponents of the same bases, simplify the fractions individually, and then multiply the simplified parts. The final simplified expression is 1/100.
Step-by-step explanation:
To simplify the given expression: 3^5×10^5×25/5^7×6^5, we can start by dividing the exponents of the same bases. For example, 3^5/3^7 = 3^(5-7) = 3^(-2) = 1/3^2 = 1/9. Similarly, we can simplify 10^5/5^7 as 10^5/(2^7×5^5) = (2^5×5^5)/(2^7×5^5) = 2^(5-7) = 2^(-2) = 1/2^2 = 1/4. Lastly, 6^5/5^7 can be simplified as 6^5/(2^7×5^5) = (2^5×3^5)/(2^7×5^5) = (3^5)/(2^2×5^2) = (3/5)^2 = 9/25. Now, we can simplify the entire expression by multiplying the simplified parts: (1/9)×(1/4)×(9/25) = 1/100
Learn more about Simplifying Exponents