(((10 p)/(9r^(5))))/(((5p^(7))/(3r^(2)))) Which expression is equivalent to the given quotient for all p > 2 and r < -2 ? Choose 1 answer: (A) (2)/(3r^(3)p^(6)) (B) (2p^(6))/(3r^(3)) (C) (3r^(3)p^(6))/(2) (D) (3r^(3))/(2p^(6))

Write and Simplify Expression: Write down the original expression and simplify it by dividing the numerators and denominators separately. The original expression is: \[\left(\frac{10p}{9r^5}\right) \div \left(\frac{5p^7}{3r^2}\right)\] To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction. So, we get: \[\frac{10p}{9r^5} \times \frac{3r^2}{5p^7}\]Multiply Numerators and Denominators: Multiply the numerators and denominators. Multiplying the numerators (10p and 3r^2) gives us 30pr^2. Multiplying the denominators (9r^5 and 5p^7) gives us 45p^7r^5. So, we have: \[\frac{30pr^2}{45p^7r^5}\]Cancel Common Factors: Simplify the expression by canceling out common factors. Both the numerator and the denominator have common factors of p and r. We can cancel out p from the numerator with one p from the denominator, and r^2 from the numerator with r^2 from the denominator. This gives us: \[\frac{30}{45p^6r^3}\]Divide by Greatest Common Divisor: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15. \[\frac{30 \div 15}{45p^6r^3 \div 15}\] This simplifies to: \[\frac{2}{3p^6r^3}\]Rearrange Terms: Rearrange the terms to match the answer choices. The expression \[\frac{2}{3p^6r^3}\] can be rewritten as: \[\frac{2}{3r^3p^6}\]Match with Answer Choices: Match the simplified expression to the answer choices. The expression \[\frac{2}{3r^3p^6}\] matches with choice (A).

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(((10 p)/(9r^(5))))/(((5p^(7))/(3r^(2))))
Which expression is equivalent to the given quotient for all
p > 2 and
r < -2 ?
Choose 1 answer:
(A)
(2)/(3r^(3)p^(6))
(B)
(2p^(6))/(3r^(3))
(C)
(3r^(3)p^(6))/(2)
(D)
(3r^(3))/(2p^(6))

$\frac{\left(\frac{10 p}{9 r^{5}}\right)}{\left(\frac{5 p^{7}}{3 r^{2}}\right)}$ $\newline$ Which expression is equivalent to the given quotient for all p>2 and r<-2 ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{2}{3 r^{3} p^{6}}$ $\newline$ (B) $\frac{2 p^{6}}{3 r^{3}}$ $\newline$ (C) $\frac{3 r^{3} p^{6}}{2}$ $\newline$ (D) $\frac{3 r^{3}}{2 p^{6}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\frac{\left(\frac{10 p}{9 r^{5}}\right)}{\left(\frac{5 p^{7}}{3 r^{2}}\right)}

\newline

Which expression is equivalent to the given quotient for all

p>2

and

r<-2

\newline

Choose

1

answer:

\newline

(A)

\frac{2}{3 r^{3} p^{6}}

\newline

(B)

\frac{2 p^{6}}{3 r^{3}}

\newline

(C)

\frac{3 r^{3} p^{6}}{2}

\newline

(D)

\frac{3 r^{3}}{2 p^{6}}

Write and Simplify Expression: Write down the original expression and simplify it by dividing the numerators and denominators separately. $\newline$ The original expression is: $\newline$ $\left(\frac{10p}{9r^5}\right) \div \left(\frac{5p^7}{3r^2}\right)$ $\newline$ To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction. $\newline$ So, we get: $\newline$ $\frac{10p}{9r^5} \times \frac{3r^2}{5p^7}$
Multiply Numerators and Denominators: Multiply the numerators and denominators. $\newline$ Multiplying the numerators ( $10$ p and $3$ r^ $2$ ) gives us $30$ pr^ $2$ . $\newline$ Multiplying the denominators ( $9$ r^ $5$ and $5$ p^ $7$ ) gives us $45$ p^ $7$ r^ $5$ . $\newline$ So, we have: $\newline$ $\frac{30pr^2}{45p^7r^5}$
Cancel Common Factors: Simplify the expression by canceling out common factors. $\newline$ Both the numerator and the denominator have common factors of p and r. We can cancel out p from the numerator with one p from the denominator, and r^ $2$ from the numerator with r^ $2$ from the denominator. $\newline$ This gives us: $\newline$ $\frac{30}{45p^6r^3}$
Divide by Greatest Common Divisor: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $15$ . $\newline$ $\frac{30 \div 15}{45p^6r^3 \div 15}$ $\newline$ This simplifies to: $\newline$ $\frac{2}{3p^6r^3}$
Rearrange Terms: Rearrange the terms to match the answer choices. $\newline$ The expression $\frac{2}{3p^6r^3}$ can be rewritten as: $\newline$ $\frac{2}{3r^3p^6}$
Match with Answer Choices: Match the simplified expression to the answer choices. $\newline$ The expression $\frac{2}{3r^3p^6}$ matches with choice (A).