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Directions: Simplify the follow- 26 1.. 2. 4. r s³t4 s²t² 3m2 3.9°r²s q²rs 5. x²y² z x²y²z m³n²o m²n²o

Directions: Simplify the follow- 26 1.. 2. 4. r s³t4 s²t² 3m2 3.9°r²s q²rs 5. x²y² z x²y²z m³n²o m²n²o

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Simplifying Algebraic Fractions Below are a series of algebraic fractions that can be simplified. Simplify each fraction by applying the properties of exponents and the rules of fractions. 6. \(\frac{x^2}{x}\) - Simplify by subtracting the exponents of \(x\). 7. \(\frac{z^4}{z^5}\) - Simplify by subtracting the exponents of \(z\). 8. \(\frac{a^2b^2}{ab^2}\) - Simplify by dividing the numerator by the denominator, canceling out the common terms. 9. \(\frac{d^5 f^3}{df}\) - Simplify by dividing the numerator by the denominator, canceling out the common terms. 10. \(\frac{mn^2}{mn^2}\) - Simplify by canceling out the common terms in the numerator and the denominator. Detailed solutions: #### 6. Simplification of \(\frac{x^2}{x}\) \[ \frac{x^2}{x} = \frac{x \cdot x}{x} = x^{2-1} = x \] #### 7. Simplification of \(\frac{z^4}{z^5}\) \[ \frac{z^4}{z^5} = \frac{z \cdot z \cdot z \cdot z}{z \cdot z \cdot z \cdot z \cdot z} = z^{4-5} = z^{-1} = \frac{1}{z} \] #### 8. Simplification of \(\frac{a^2b^2}{ab^2}\) \[ \frac{a^2 b^2}{a b^2} = \frac{a \cdot a \cdot b \cdot b}{a \cdot b \cdot b} = a^{2-1} \cdot b^{2-2} = a \cdot 1 = a \] #### 9. Simplification of \(\frac{d^5 f^3}{df}\) \[ \frac{d^5 f^3}{d f} = \frac{d \cdot d \cdot d \cdot d \cdot
Transcribed Image Text:### Simplifying Algebraic Fractions Below are a series of algebraic fractions that can be simplified. Simplify each fraction by applying the properties of exponents and the rules of fractions. 6. \(\frac{x^2}{x}\) - Simplify by subtracting the exponents of \(x\). 7. \(\frac{z^4}{z^5}\) - Simplify by subtracting the exponents of \(z\). 8. \(\frac{a^2b^2}{ab^2}\) - Simplify by dividing the numerator by the denominator, canceling out the common terms. 9. \(\frac{d^5 f^3}{df}\) - Simplify by dividing the numerator by the denominator, canceling out the common terms. 10. \(\frac{mn^2}{mn^2}\) - Simplify by canceling out the common terms in the numerator and the denominator. Detailed solutions: #### 6. Simplification of \(\frac{x^2}{x}\) \[ \frac{x^2}{x} = \frac{x \cdot x}{x} = x^{2-1} = x \] #### 7. Simplification of \(\frac{z^4}{z^5}\) \[ \frac{z^4}{z^5} = \frac{z \cdot z \cdot z \cdot z}{z \cdot z \cdot z \cdot z \cdot z} = z^{4-5} = z^{-1} = \frac{1}{z} \] #### 8. Simplification of \(\frac{a^2b^2}{ab^2}\) \[ \frac{a^2 b^2}{a b^2} = \frac{a \cdot a \cdot b \cdot b}{a \cdot b \cdot b} = a^{2-1} \cdot b^{2-2} = a \cdot 1 = a \] #### 9. Simplification of \(\frac{d^5 f^3}{df}\) \[ \frac{d^5 f^3}{d f} = \frac{d \cdot d \cdot d \cdot d \cdot
### Simplifying Algebraic Expressions #### Directions: Simplify the following expressions. 1. \(\dfrac{r^6}{r}\) 2. \(\dfrac{s^3 t^4}{s^2 t^2}\) 3. \(\dfrac{q^3 r^2 s}{q^2 r s}\) 4. \(\dfrac{x^2 y^2 z}{x^2 y^2 z}\) 5. \(\dfrac{m^3 n^2 o}{m^2 n^2 o}\) ### Detailed Solution Guide: 1. \(\dfrac{r^6}{r}\) - Use the property of exponents \(\dfrac{a^m}{a^n} = a^{m-n}\). - Simplify: \(r^{6-1} = r^5\). 2. \(\dfrac{s^3 t^4}{s^2 t^2}\) - Apply the property of exponents to each variable separately. - Simplify \(s\): \(s^{3-2} = s^1 = s\). - Simplify \(t\): \(t^{4-2} = t^2\). - Combined result: \(st^2\). 3. \(\dfrac{q^3 r^2 s}{q^2 r s}\) - Apply the property of exponents to each variable separately. - Simplify \(q\): \(q^{3-2} = q^1 = q\). - Simplify \(r\): \(r^{2-1} = r\). - Simplify \(s\): The \(s\) terms cancel out. - Combined result: \(qr\). 4. \(\dfrac{x^2 y^2 z}{x^2 y^2 z}\) - Any expression divided by itself equals 1. - Simplified result: 1. 5. \(\dfrac{m^3 n^2 o}{m^2 n^2 o}\) - Apply the property of exponents to each variable separately. - Simplify \(m\): \(m^{3-2} = m\). - Simplify \(n\): The \(n\) terms cancel out. - Simplify \(o\
Transcribed Image Text:### Simplifying Algebraic Expressions #### Directions: Simplify the following expressions. 1. \(\dfrac{r^6}{r}\) 2. \(\dfrac{s^3 t^4}{s^2 t^2}\) 3. \(\dfrac{q^3 r^2 s}{q^2 r s}\) 4. \(\dfrac{x^2 y^2 z}{x^2 y^2 z}\) 5. \(\dfrac{m^3 n^2 o}{m^2 n^2 o}\) ### Detailed Solution Guide: 1. \(\dfrac{r^6}{r}\) - Use the property of exponents \(\dfrac{a^m}{a^n} = a^{m-n}\). - Simplify: \(r^{6-1} = r^5\). 2. \(\dfrac{s^3 t^4}{s^2 t^2}\) - Apply the property of exponents to each variable separately. - Simplify \(s\): \(s^{3-2} = s^1 = s\). - Simplify \(t\): \(t^{4-2} = t^2\). - Combined result: \(st^2\). 3. \(\dfrac{q^3 r^2 s}{q^2 r s}\) - Apply the property of exponents to each variable separately. - Simplify \(q\): \(q^{3-2} = q^1 = q\). - Simplify \(r\): \(r^{2-1} = r\). - Simplify \(s\): The \(s\) terms cancel out. - Combined result: \(qr\). 4. \(\dfrac{x^2 y^2 z}{x^2 y^2 z}\) - Any expression divided by itself equals 1. - Simplified result: 1. 5. \(\dfrac{m^3 n^2 o}{m^2 n^2 o}\) - Apply the property of exponents to each variable separately. - Simplify \(m\): \(m^{3-2} = m\). - Simplify \(n\): The \(n\) terms cancel out. - Simplify \(o\
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