Final answer:
To simplify (10z⁵ - 6z²) x 9z⁴, distribute 9z⁴ to each term to get 90z⁹ - 54z⁶. The exponents are added when multiplying terms with the same base.
Step-by-step explanation:
The student is asking to simplify the algebraic expression (10z⁵ - 6z²) x 9z⁴. To simplify this expression, we need to use the distributive property to multiply each term inside the parentheses by 9z⁴. Here's the step-by-step process:
- Multiply 10z⁵ by 9z⁴ to get 90z⁹ (when multiplying exponents with the same base, you add the exponents).
- Multiply -6z² by 9z⁴ to get -54z⁶ (again, add the exponents).
So, the simplified expression is 90z⁹ - 54z⁶.
Check the answer to ensure it is reasonable:
- The exponents have been correctly added.
- The coefficients have been correctly multiplied.