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Chapter 0: Problem 107

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\frac{\left(x^{-2} y\right)^{-3}}{\left(x^{2} y^{-1}\right)^{3}}$$

Short Answer

Expert verified
The expression simplifies to \(x^{-12}\)

Step by step solution

01

Apply the Power Rule (a^(m*n) = a^(m)*a^(n))

The expression can be rewritten as: \((x^(-2*3) y^(-3)) / (x^(2*3) y^(-1*3))\). Therefore the expression becomes: \((x^{-6}y^{-3}) / (x^{6} y^{-3})\)
02

Use Law of Exponents to Combine Like Terms (a^m / a^n = a^(m-n))

This simplifies the expression to: \(x^{(-6-6)} y^{(-3-(-3))}\). Then the expression becomes: \(x^{-12} y^0\)
03

Simplify the Expression

Any nonzero number to the power of zero is 1. Hence: \(y^0 = 1\). The final simplification of the expression is: \(x^{-12}*1\)

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