Evaluate. 3^8a^10b^-5c^2/3^12a^7b^-3c^-2
a=4, b= 8 c=3
3^8 a^10 b^-5 c^2
----------------------
3^12 a^7 b^-3 c^-2
a^3 c^4
-----------
3^4 b^2
4^3 3^4
---------- = 4^3/8^2 = 1
3^4 8^2
To evaluate the given expression, we substitute the values of a, b, and c into the expression and simplify.
Step 1: Substitute the values of a, b, and c into the expression:
3^8 * a^10 * b^-5 * c^2 / 3^12 * a^7 * b^-3 * c^-2
Replacing a with 4, b with 8, and c with 3:
3^8 * 4^10 * 8^-5 * 3^2 / 3^12 * 4^7 * 8^-3 * 3^-2
Step 2: Simplify each term:
Using the exponent rules, we can simplify:
3^8 = 6561
4^10 = 1048576
8^-5 = 1/32768
3^2 = 9
3^12 = 531441
4^7 = 16384
8^-3 = 1/512
3^-2 = 1/9
Now, the expression becomes:
6561 * 1048576 * (1/32768) * 9 / (531441) * 16384 * (1/512) * (1/9)
Step 3: Multiply and divide:
To simplify further, we multiply the numerators and the denominators:
(6561 * 1048576 * 9 * 16384) / (32768 * 531441 * 512 * 9)
Simplifying:
(611729611264 * 147456) / (176947200512 * 9)
Step 4: Cancel out common factors:
In this step, we can simplify the expression further by canceling out common factors in the numerator and denominator:
611729611264 / 176947200512
Now, we are left with a simplified numerical value.
Step 5: Divide:
Dividing these numbers, we get the final result:
3.459770115368215
Therefore, the evaluated value of the given expression, when a = 4, b = 8, and c = 3, is approximately 3.459770115368215.