If 4 = 10^2m and 9 = 10^2n, then 0.15 equals to :

To find the value of 0.15 in terms of m and n, we use the given equations 4 = 10^(2m) and 9 = 10^(2n). Taking the square root of both sides, we get 2 = 10^m and 3 = 10^n. The value 0.15 can be expressed as the fraction 15/100, which simplifies to 3/20. Further, 3/20 can be written as 3 / (2 * 10). Substituting the powers of 10 derived earlier, we get 10^n / (10^m * 10^1). According to the laws of exponents [t1][t4], when dividing powers with the same base, we subtract the exponents: 10^(n - m - 1). This matches option 4. Scientific notation and exponential rules confirm that 10 raised to a negative power represents small decimal values [t4]. Thus, 0.15 equals 10^(n-m-1).

Sources

1. [1] https://www.mathcentre.ac.uk/resources/uploaded/hobsonajjustthemaths20021296smcetp.pdf