Question

2^n * 6^m+1 * 10^m-n * 15^m+n-2 divided by 4^m * 3^2m+n * 25^m-1

Answer 1

Answer:

2/3

Step-by-step explanation:

Given  

2^n * 6^m+1 * 10^m-n * 15^m+n-2 divided by 4^m * 3^2m+n * 25^m-1

Now we need to apply law of exponents a^m x a^n = a^m + n and a^m / a^n = a^m – n

2^n x 2^m + 1 x 3^m + 1 x 2 ^m – n x 5^m – n x 3^m + n – 2 x 5^m + n – 2 / 2^m x 2^m x 3^2m + n x 5^m – 1 x 5^m – 1

2^n + m + 1 + m – n x 3 ^m + 1 + m + n – 2 x 5^m – n + m + n – 2 / 2^m + m x 3 ^2m + n x 5^m – 1 + m – 1

2^2m + 1  x 3^2m + n – 2 x 5^2m – 2 / 2^2m x 3^2m + n x 5 ^2m – 2

2^2m + 1 – 2m x 3^2m + n – 1 – 2m – n  

2^1 x 3^-1

= 2 / 3

Answer 2

Final answer is 2/3