Final answer:
The value of m in the equation 511 = 52 x⁵m is found by setting 52 x 59 = 52 x⁵m and solving for m, giving m = 9 / 5 = 1.8, which does not match any of the provided options.
Step-by-step explanation:
To find the value of m in the equation 511 = 52 x⁵m, we need to understand the properties of exponents. First, we recognize that the bases on both sides of the equation must be the same for the equation to be true. Since 511 can be expressed as 52 x 59, we can set up an equation where 52 x 59 = 52 x⁵m.
By comparing exponents of the same base, we can deduce that 5m = 9. To find the value of m, we simply divide both sides of the equation by 5: m = 9 / 5 = 1.8. Since 1.8 is not one of the choices provided A. 3, B. 5.5, C. 9, D. 12.5, it appears there might have been a misunderstanding in the question. Nevertheless, based on the information given, m equals 1.8.