**Q: Simplify (4x^6+8y^4) / (16x).**

A: Many different methods exist!

**Method 1**

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)

**Method 2**

(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.