Final answer:
The expression x^18 - y^10 can be correctly expressed in simplest form as (x^2)^9 - (y^2)^5, since this preserves the original exponents of x and y without altering the meaning of the expression.
Step-by-step explanation:
To express the expression x^18 − y^10 in simplest form, we need to look at the given options:
- (a) x^8 - y^10
- (b) x^10 - y^18
- (c) (x^2)^9 - (y^2)^5
- (d) (x^9)^2 - (y^5)^2
Options (a) and (b) are incorrect because they alter the exponents of x and y, thus changing the meaning of the expression. Option (c) is the correct answer because it's a matter of expressing the given powers as powers of a power, which does not change the value. Therefore, (x^2)^9 is the same as x^(2*9) = x^18, and similarly, (y^2)^5 is the same as y^(2*5) = y^10.
The correct expression in simplest form is thus (x^2)^9 - (y^2)^5.