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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 simplified exponential expression is 1

Step by step solution

01

Apply the power of a power property

The power of a power property states that \((a^m)^n = a^{m*n}\). So, we will simplify \((x^{-2} y)^{-3}\) as \(x^{-2*-3} y^{-3}\) and \((x^{2} y^{-1})^{3}\) as \(x^{2*3} y^{-1*3}\), which results in \(\frac{x^{6} y^{-3}}{x^{6} y^{-3}}\)
02

Apply the power of a quotient property

This rule says that \(\frac{a^n}{b^n} = (\frac{a}{b})^n\). So, we apply this to revise the expression to \(\frac{x^{6}}{x^{6}} * \frac{y^{-3}}{y^{-3}}\)
03

Apply the quotient of powers with the same base rule

This rule states that \(\frac{a^n}{a^m} = a^{n-m}\). We'll use this to simplify \(\frac{x^{6}}{x^{6}}\) to \(x^{6-6}\) and \(\frac{y^{-3}}{y^{-3}}\) to \(y^{-3-(-3)}\), which simplifies to \(x^{0}*y^{0}\)
04

Apply the zero exponent rule

The zero exponent rule states that, for any nonzero number, the number to the zero exponent equals 1. So, \(x^{0}*y^{0}\) simplifies to \(1*1 = 1\)

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Most popular questions from this chapter

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