Answer:
To divide the expression \(81(p^4q^2r^3 + 2p^3q^3r^2 - 5p^2q^2r^2)\) by \((3pqr)^2\), you can simplify both the numerator and denominator first.
Step-by-step explanation:
1. First, simplify \((3pqr)^2\):
\((3pqr)^2 = 9p^2q^2r^2\).
2. Now, rewrite the expression with the simplified denominator:
\(\frac{81(p^4q^2r^3 + 2p^3q^3r^2 - 5p^2q^2r^2)}{9p^2q^2r^2}\).
3. Next, divide each term in the numerator by the denominator:
\(\frac{81}{9}\cdot \frac{p^4q^2r^3}{p^2q^2r^2} + \frac{81}{9}\cdot \frac{2p^3q^3r^2}{p^2q^2r^2} - \frac{81}{9}\cdot \frac{5p^2q^2r^2}{p^2q^2r^2}\).
4. Simplify each term:
\(\frac{9}{1}\cdot \frac{p^(4-2)q^(2-2)r^(3-2)}{1} + \frac{9}{1}\cdot \frac{2p^(3-2)q^(3-2)r^(2-2)}{1} - \frac{9}{1}\cdot \frac{5p^(2-2)q^(2-2)r^(2-2)}{1}\).
5. Further simplify:
\(9p^2r + 18q - 45\).
So, the simplified result of dividing \(81(p^4q^2r^3 + 2p^3q^3r^2 - 5p^2q^2r^2)\) by \((3pqr)^2\) is \(9p^2r + 18q - 45\).
[tex] \frac{81( {p}^{4} {q}^{2} {r}^{3} + 2 {p}^{3} {q}^{3} {r}^{2} - 5 {p}^{2} {q}^{2} {r}^{2} ) }{ {(3pqr)}^{2} } [/tex]
[tex] \frac{81( {p}^{4} {q}^{2} {r}^{3} + 2 {p}^{3} {q}^{3} {r}^{2} - 5 {p}^{2} {q}^{2} {r}^{2} ) }{ 9{p}^{2} {q}^{2} {r}^{2} } [/tex]
[tex] \frac{9( {p}^{4} {q}^{2} {r}^{3} + 2 {p}^{3} {q}^{3} {r}^{2} - 5 {p}^{2} {q}^{2} {r}^{2} ) }{ {p}^{2} {q}^{2} {r}^{2} } [/tex]
[tex] = 9( \frac{ {p}^{4} {q}^{2} {r}^{3} }{ {p}^{2} {q}^{2} {r}^{2} } + \frac{2 {p}^{3} {q}^{3} {r}^{2} }{{p}^{2} {q}^{2} {r}^{2}} - \frac{5 {p}^{2} {q}^{2} {r}^{2} }{{p}^{2} {q}^{2} {r}^{2}} )[/tex]
= 9(p²r + 2pq - 5)
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Answers & Comments
Verified answer
Answer:
To divide the expression \(81(p^4q^2r^3 + 2p^3q^3r^2 - 5p^2q^2r^2)\) by \((3pqr)^2\), you can simplify both the numerator and denominator first.
Step-by-step explanation:
To divide the expression \(81(p^4q^2r^3 + 2p^3q^3r^2 - 5p^2q^2r^2)\) by \((3pqr)^2\), you can simplify both the numerator and denominator first.
1. First, simplify \((3pqr)^2\):
\((3pqr)^2 = 9p^2q^2r^2\).
2. Now, rewrite the expression with the simplified denominator:
\(\frac{81(p^4q^2r^3 + 2p^3q^3r^2 - 5p^2q^2r^2)}{9p^2q^2r^2}\).
3. Next, divide each term in the numerator by the denominator:
\(\frac{81}{9}\cdot \frac{p^4q^2r^3}{p^2q^2r^2} + \frac{81}{9}\cdot \frac{2p^3q^3r^2}{p^2q^2r^2} - \frac{81}{9}\cdot \frac{5p^2q^2r^2}{p^2q^2r^2}\).
4. Simplify each term:
\(\frac{9}{1}\cdot \frac{p^(4-2)q^(2-2)r^(3-2)}{1} + \frac{9}{1}\cdot \frac{2p^(3-2)q^(3-2)r^(2-2)}{1} - \frac{9}{1}\cdot \frac{5p^(2-2)q^(2-2)r^(2-2)}{1}\).
5. Further simplify:
\(9p^2r + 18q - 45\).
So, the simplified result of dividing \(81(p^4q^2r^3 + 2p^3q^3r^2 - 5p^2q^2r^2)\) by \((3pqr)^2\) is \(9p^2r + 18q - 45\).
Answer:
[tex] \frac{81( {p}^{4} {q}^{2} {r}^{3} + 2 {p}^{3} {q}^{3} {r}^{2} - 5 {p}^{2} {q}^{2} {r}^{2} ) }{ {(3pqr)}^{2} } [/tex]
[tex] \frac{81( {p}^{4} {q}^{2} {r}^{3} + 2 {p}^{3} {q}^{3} {r}^{2} - 5 {p}^{2} {q}^{2} {r}^{2} ) }{ 9{p}^{2} {q}^{2} {r}^{2} } [/tex]
[tex] \frac{9( {p}^{4} {q}^{2} {r}^{3} + 2 {p}^{3} {q}^{3} {r}^{2} - 5 {p}^{2} {q}^{2} {r}^{2} ) }{ {p}^{2} {q}^{2} {r}^{2} } [/tex]
[tex] = 9( \frac{ {p}^{4} {q}^{2} {r}^{3} }{ {p}^{2} {q}^{2} {r}^{2} } + \frac{2 {p}^{3} {q}^{3} {r}^{2} }{{p}^{2} {q}^{2} {r}^{2}} - \frac{5 {p}^{2} {q}^{2} {r}^{2} }{{p}^{2} {q}^{2} {r}^{2}} )[/tex]
= 9(p²r + 2pq - 5)