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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblema 107
Capitolo 1, Problema 107

Simplify each exponential expression. Assume that variables represent nonzero real numbers. (x−2y)−3(x2y−1)3\(\frac{(x^{-2}\) y)^{-3}}{(x^{2} y^{-1})^{3}}

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Start by rewriting the given expression clearly: \(\frac{(x^{-2} y)^{-3}}{(x^{2} y^{-1})^{3}}\).
Apply the power of a power rule, which states that \((a^{m})^{n} = a^{m \times n}\), to both the numerator and the denominator separately.
For the numerator: \((x^{-2} y)^{-3} = x^{-2 \times (-3)} y^{1 \times (-3)} = x^{6} y^{-3}\).
For the denominator: \((x^{2} y^{-1})^{3} = x^{2 \times 3} y^{-1 \times 3} = x^{6} y^{-3}\).
Rewrite the expression as \(\frac{x^{6} y^{-3}}{x^{6} y^{-3}}\) and then apply the quotient rule for exponents, which states \(\frac{a^{m}}{a^{n}} = a^{m-n}\), to simplify the expression.

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A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, x^(-n) equals 1/x^n. Recognizing and correctly applying this rule helps simplify expressions with negative powers by rewriting them as fractions.
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