Typical problems in this homework set cover five key operation types:
When dividing terms with the same base, you keep the base and the exponents. $$\fracx^ax^b = x^a-b$$
| | Example | Correct Way | |-------------|-------------|------------------| | Adding exponents in addition/subtraction | ( 3x^2 + 4x^2 = 7x^4 ) ❌ | Only add coefficients: ( 7x^2 ) ✅ | | Multiplying exponents in multiplication | ( x^3 \cdot x^4 = x^12 ) ❌ | Add exponents: ( x^7 ) ✅ | | Forgetting coefficient powers | ( (3x^2)^3 = 3x^6 ) ❌ | Raise coefficient: ( 27x^6 ) ✅ | | Ignoring negative signs | ( (-2)^2 = -4 ) ❌ | ( (-2)^2 = +4 ) ✅ | unit 6 homework 5 monomials all operations answer key
Many problems on this worksheet combine these steps (e.g., multiplying in the numerator and then dividing). When using your , follow the PEMDAS order: Parentheses: Handle "Power of a Power" first. Multiply/Divide: Move from left to right. Add/Subtract: Save this for the very last step. Summary Checklist for Your Homework Did I keep exponents the same when adding/subtracting? Did I add exponents when multiplying? Did I subtract exponents when dividing?
When you multiply monomials, you are combining everything together. Typical problems in this homework set cover five
Simplify: $8x^3 - 2x^3$
( \frac(5y^3)^210y^4 ) Answer: ( 2.5y^2 ) or ( \frac52y^2 ) Explanation: Numerator: 25y⁶. Divide: 25÷10 = 2.5; subtract exponents 6-4=2. Multiply/Divide: Move from left to right
When a monomial is raised to an exponent, the exponents multiply in a frantic burst of growth. 🔑 The Answer Key: Common Solutions