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Question

Part 1
Use the power​ rule, the power of a product​ rule, and the power of a quotient rule to simplify the expression.
(7x^2z/y^3)^3=

Answer 1

To simplify the expression (7x^2z/y^3)^3 using the power rule, the power of a product rule, and the power of a quotient rule, we can break it down step by step.

First, let's apply the power rule to (7x^2z/y^3) raised to the power of 3:
(7x^2z/y^3)^3 = (7^3 * (x^2)^3 * z^3) / (y^3)^3

Next, let's simplify the exponents using the power of a product rule and the power of a quotient rule:
(7^3 * (x^2)^3 * z^3) / (y^3)^3 = 343 * x^(2*3) * z^3 / y^(3*3)

Simplifying the exponents, we have:
343 * x^6 * z^3 / y^9

So, the simplified expression is 343x^6z^3 / y^9.