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Chapter 0: Problem 59

Simplify each exponential expression. $$\left(\frac{5 x^{3}}{y}\right)^{-2}$$

Short Answer

Expert verified
The simplified form of \(\left(\frac{5 x^{3}}{y}\right)^{-2}\) is \(\frac{y^2}{25x^6}\).

Step by step solution

01

Distribute the Exponent

Start by distributing the exponent -2 to each part of the fraction in the base. This results in \((5^{-2})(x^{3*-2})/(y^{-2})\).
02

Calculate the Negative Exponents

Now, remember that a negative exponent simply inverts the base, i.e, \(a^{-n} = \frac{1}{a^n}\). With this rule, replace each part with negative exponents, getting \(\frac{1}{5^2}*\frac{1}{x^{3*2}}*y^2\).
03

Simplify the Expression

Now calculate the remaining exponents and simplify the result into simplest terms. This gives: \(\frac{1}{25}*\frac{1}{x^{6}}*y^2\), which simplifies to \(\frac{y^2}{25x^6}\).

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