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Chapter 5: Problem 12

Simplify (a) \(x^{2} x^{5} x^{9}\), (b) \(\frac{x^{9}}{x^{4}}\), (c) \(\frac{x^{4}}{x^{5}}\).

Short Answer

Expert verified
Question: Simplify the following expressions: (a) \(x^{2} x^{5} x^{9}\), (b) \(\frac{x^{9}}{x^{4}}\), and (c) \(\frac{x^{4}}{x^{5}}\). Answer: The simplified expressions are: (a) \(x^{16}\), (b) \(x^{5}\), and (c) \(x^{-1}\).

Step by step solution

01

(a) Simplify \(x^{2} x^{5} x^{9}\)

To simplify the expression, we will use the product rule. Combine all the exponents by adding them together. \(x^{2} x^{5} x^{9} = x^{(2+5+9)}\) Now, add the exponents: \(x^{(2+5+9)} = x^{16}\) So, the simplified expression is \(x^{16}\).
02

(b) Simplify \(\frac{x^{9}}{x^{4}}\)

In order to simplify the expression, we will apply the quotient rule. Subtract the exponent of the denominator from the exponent of the numerator. \(\frac{x^{9}}{x^{4}} = x^{(9-4)}\) Now, subtract the exponents: \(x^{(9-4)} = x^{5}\) So, the simplified expression is \(x^{5}\).
03

(c) Simplify \(\frac{x^{4}}{x^{5}}\)

To simplify this expression, we will use the quotient rule as well. Subtract the exponent of the denominator from the exponent of the numerator. \(\frac{x^{4}}{x^{5}} = x^{(4-5)}\) Subtract the exponents: \(x^{(4-5)} = x^{-1}\) So, the simplified expression is \(x^{-1}\).

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