Final answer:
To evaluate 214 25÷(−12)-¹⁴, divide 214 by 25 and then divide the result by -12. To get the final answer as a mixed number in simplest form, divide 1 by the previous result and simplify.
Step-by-step explanation:
To evaluate the expression 214 25÷(−12)-¹⁴, we can follow the rules of exponents. First, let's simplify the exponent. When we have a negative exponent, we can rewrite it as the reciprocal of the positive exponent. So, (-12)-¹⁴ becomes 1/((-12)¹⁴). Now, let's simplify the expression inside the parentheses. 214 25÷(-12) would be calculated from left to right as follows:
- Divide 214 by 25 to get 8.56
- Divide 8.56 by (-12) to get -0.71333...
Now, we can rewrite the original expression as 1/(-0.71333...). To convert this to a mixed number in simplest form, we divide 1 by -0.71333... and simplify:
- -1 ÷ 0.71333... = -1.40137...
Therefore, the mixed number in simplest form is -1⅔.