Question

Simplify
`(9x^(16) )/(6(x^(2) )^(3)x^(2) ) }`

Answer 1

`\displaystyle (3x^8)/(2)`

General Formulas and Concepts:

Algebra I

• Exponential Rule [Multiplying]:
  `\displaystyle b^m \cdot b^n = b^(m + n)`
• Exponential Rule [Dividing]:
  `\displaystyle (b^m)/(b^n) = b^(m - n)`
• Exponential Rule [Powering]:
  `\displaystyle (b^m)^n = b^(m \cdot n)`
• Exponential Rule [Rewrite]:
  `\displaystyle b^(-m) = (1)/(b^m)`

Explanation:

Step 1: Define

Identify

`\displaystyle (9x^(16))/(6(x^2)^3x^2)`

Step 2: Simplify

1. Exponential Rule [Powering]:
   `\displaystyle (9x^(16))/(6x^6x^2)`
2. Exponential Rule [Multiplying]:
   `\displaystyle (9x^(16))/(6x^8)`
3. Exponential Rule [Dividing]:
   `\displaystyle (9x^8)/(6)`
4. Simplify:
   `\displaystyle (3x^8)/(2)`