Q: Simplify (4x^6+8y^4) / (16x).
A: Many different methods exist!
This is the same as:
4x^6 / (16x) + 8y^4 / (16x)
Reduce the numbers and the letters where possible:
(1) 4x^6 / (16x) [reduce the 4 and the 16 and take one x out of the top an bottom]
= x^5 / 4 or 1/4 x^5
(2) 8y^4 / (16x) [only the 8 and 16 can reduce]
= y^4 / (2x)
So, (4x^6+8y^4) / (16x) = x^5 / 4 + y^4 / (2x)
(4x^6+8y^4) / (16x)
Factor the top to reduce like terms in the end:
4(x^6 + 2y^4) / (16x)
Reduce the fraction:
(x^6 + 2y^4) / (4x),
Method 3: Using negative exponents
(4x^6 + 8y^4) / (16x) =
4x^6 / (16x) + 8y^4 / (16x) [Reduce the numbers. Then, subtract the exponent of the x in the denominator from the exponent of the x in the numerator. If there is no x in the numerator, the exponent will be negative]
(1/4)x^(6-1) + (1/2)y^4*x^-1 =
(1/4)x^5 + (1/2)y^4*x^-1.