Question

Multiply: x^2×y^2 × mn / x^11

Answer 1

Answer:

Answer: |

1/(a b x y)

Step-by-step explanation:

Simplify the following:

(x^2 y^2 m n x^8 y^9 m n)/(x^11 y^12 m^2 n^2 a b)

Combine powers. (m n x^8 y^9 m n x^2 y^2)/(a b m^2 n^2 x^11 y^12) = (m^(1 + 1 - 2) n^(1 + 1 - 2) x^(8 + 2 - 11) y^(9 + 2 - 12))/(a b):

(m^(1 + 1 - 2) n^(1 + 1 - 2) x^(8 + 2 - 11) y^(9 + 2 - 12))/(a b)

1 + 1 - 2 = 0:

(m^0 n^(1 + 1 - 2) x^(8 + 2 - 11) y^(9 + 2 - 12))/(a b)

1 + 1 - 2 = 0:

(m^0 n^0 x^(8 + 2 - 11) y^(9 + 2 - 12))/(a b)

8 + 2 - 11 = -1:

(m^0 n^0 x^(-1) y^(9 + 2 - 12))/(a b)

9 + 2 - 12 = -1:

(m^0 n^0 y^(-1))/(x a b)

n^0 = 1:

m^0/(a b x y)

m^0 = 1:

Answer 2

Step-by-step explanation:

$\sf{Given \: that:}$

$\sf\frac{ {x}^{2} \times {y}^{2} \times mn}{ {x}^{11} {y}^{12} {m}^{2} {n}^{2} } \times \frac{ {x}^{8} {y}^{9} mn}{ab}$

$\sf = \frac{ {x}^{2} \times {x}^{8} \times {y}^{3} \times {y}^{9} \times m \times m \times n \times n }{ {x}^{11} \times {x}^{12} \times {m}^{2} \times {n}^{2} \times ab}$

$[ \sf\because\: {a}^{m} \times {a}^{n} = {a}^{m + n} ]$

$\sf = \frac{( {x}^{2 + 8}) \times ( {y}^{3 + 9} ) \times ({m}^{1 + 1} ) \times ( {n}^{1 + 1} )}{ {x}^{11} \times {y}^{12} \times {m}^{2} \times ab}$

$\sf = \frac{{x}^{10} \times {y}^{12} \times {m}^{2} \times {n}^{2} }{ {x}^{11} \times {y}^{12} \times {m}^{2} \times {n}^{2} \times ab}$

$\sf = \frac{{x}^{10} \times {y}^{12} \times \cancel{ {m}^{2} } \times \cancel{ {n}^{2}} }{ {x}^{11} \times {y}^{12} \times \cancel{{m}^{2} } \times \cancel{{n}^{2} } \times ab}$

$[ \sf \because \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} ]$

$= \sf\frac{ {x}^{10 - 11} \times {y}^{12 - 12} }{ab}$

$\sf = \frac{ {x}^{ - 1} \times {y}^{0} }{ab}$

$\sf = \frac{ {x}^{ - 1} \times 1}{ab} \: \: \: [ \because {a}^{0} = 1 ]$

$\sf = \frac{ {x}^{ - 1} }{ab}$

$\sf = \frac{ {x}^{ - 1} }{ab} \: \: \: \: [ \because \: {a}^{ - n} = \frac{1}{ {a}^{n} } ]$

$= \boxed{ \sf \frac{1}{xab} }\: Ans.$

$\sf{ Let \: me \: know \: if \: you \: have \: any \: other \: questions.}$