Final answer:
To simplify (50x⁴)/(35x³), we divide the numerical parts and subtract the exponents of x, resulting in the simplified form (10x)/(7).
Step-by-step explanation:
The student is asking how to simplify the fraction (50x⁴)/(35x³). To simplify, we divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms. Since both the numerator and denominator contain the variable 'x', we can simplify by cancelling out the common factors.
First, we simplify the numerical part of the fraction. The greatest common factor of 50 and 35 is 5. Dividing both 50 and 35 by 5, we get 10 and 7, respectively. So, (50/35) simplifies to (10/7).
Next, we deal with the exponential part: (x⁴/x³). According to the division of exponentials rule, we subtract the exponents, yielding x¹ or simply x, because we don't write the subscript if it is one.
Thus, the fully simplified form of the given fraction is (10x)/(7). No further simplification is possible.