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Express x^18 – y^10 in simplest form.

a. x^8 - y^10
b. x^10 - y^18
c. (x^2)^9 - (y^2)^5
d. (x^9)^2 - (y^5)^2

User Isaac B
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1 Answer

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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.

User Suxgri
by
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