Question

Rewriting expressions using algebraic properties doesn't change the value of the expression or the relationship it describes.

Answer 1

Answer:

  see attached

Step-by-step explanation:

No doubt you have examples showing the wording that is expected to be used here. We have made a guess.

power of a ratio: the numerator is raised to the power, as is the denominator. (a/b)^c = (a^c)/(b^c)

power of a product: each factor is raised to the power. (ab)^c = (a^c)(b^c)

power of a power: the powers are multiplied. (a^b)^c = a^(bc)

quotient of powers: the result when one power is divided by another is the difference of the numerator and denominator powers. (a^b)/(a^c) = a^(b-c)

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Additional comment

The order of operations tells you to simplify inside parentheses first. Doing that reduces the work somewhat.

  $\left(\dfrac{-3x^3y}{x^2}\right)^4=(-3xy)^4=(-3)^4x^4y^4=81x^4y^4$