Final answer:
The simplified form of the expression (2z^4y^2)^5 is 32z^20y^10, applying the power of a power rule to each part of the expression separately.
Step-by-step explanation:
To simplify the expression (2z4y2)5, we need to apply the power of a power rule, which states that (am)n = am*n. For the base 2, we raise it to the power of 5: 25. For the variables, we multiply their exponents by 5: z4*5 and y2*5. After simplifying:
- 25 is 32,
- z4*5 is z20,
- y2*5 is y10.
Combining these, the simplified expression without parentheses is 32z20y10. Remember that we do not write the subscript if it is one, and we can eliminate terms wherever possible to simplify the algebra.