Which value is equivalent to 7 multiplied by 3 multiplied by 2 whole over 7 multiplied by 5, the whole raised to the power of 2 multiplied by 7 to the power of 0 over 5 to the power of negative 3, whole to the power of 3 multiplied by 5 to the power of negative 9? (1 point)
6 over 25
36 over 25
12 over 5
252 over 5
To simplify, we will work from left to right in each fraction and then simplify the exponents.
7 multiplied by 3 multiplied by 2 = 42
7 multiplied by 5 = 35
So far, we have (42/35).
Next, we simplify the exponents:
7 to the power of 0 is equal to 1.
5 to the power of -3 is equal to 1/(5^3) = 1/125.
(42/35) to the power of 2 is equal to (42^2)/(35^2) = 1764/1225.
(1/125) to the power of 3 is equal to (1^3)/(125^3) = 1/1953125.
Multiplying these values together gives:
(1764/1225) * (1/1953125) = 1764/(1225 * 1953125) = 252/(5 * 390625) = (252/5) / 390625 = 50.4/390625.
Therefore, the equivalent value is 50.4/390625.
Converting this fraction to a simplified fraction gives 36/28125.
So, the answer is 36 over 28125, which is closest to option (1) 6 over 25.