Question

plee awnsser p plpl pl

Answer 1

Answer:

100

Step-by-step explanation:

$\frac{(2 \times 5)^{4} \times {3}^{2} \times {5}^{3} }{ {5}^{5} \times (2 \times 3)^{2} } \\ = \frac{ {2}^{4} \times {5}^{4} \times {3}^{2} \times {5}^{3} }{ {5}^{5} \times {2}^{2} \times {3}^{2} } \\ = {2}^{(4 - 2)} \times {5}^{(4 + 3 - 5)} \times {3}^{(2 - 2)} \\ = {2}^{2} \times {5}^{2} \\ = {(2 \times 5)}^{2} \\ = {10}^{2} \\ = 100$

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Answer 2

$\sf{\underline{\underline{ \purple{ \large{Answer:}}}}}$

♦ 100

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$\\ \sf{\underline{\underline{ \purple{ \large{Step-by-step \: explanation:}}}}}$

$\implies \sf \dfrac{ {10}^{4} \times {3}^{2} \times 125}{ {5}^{5} \times {6}^{2} }$

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First we will expand the given terms. 10⁴ means we will expand 10 four times and multipy them with each other. Again 3² means we will expand 3 two times and multipy them with each other. Same as in the case of 5 and 6.

$\implies \sf \dfrac{ 10 \times 10 \times 10 \times 10 \times {3}^{2} \times 125}{ {5}^{5} \times {6}^{2} }$

$\\ \implies \sf \dfrac{ 10000 \times {3}^{2} \times 125}{ {5}^{5} \times {6}^{2} }$

$\\ \implies \sf \dfrac{ 10000 \times 3 \times 3 \times 125}{ {5}^{5} \times {6}^{2} }$

$\\ \implies \sf \dfrac{ 10000 \times 9 \times 125}{ {5}^{5} \times {6}^{2} }$

$\\ \implies \sf \dfrac{ 10000 \times 9 \times 125}{ 5 \times 5 \times 5 \times 5 \times 5 \times 6 \times 6 }$

$\\ \implies \sf \dfrac{ 10000 \times 9 \times 25}{ 5 \times 5 \times 5 \times 5 \times 6 \times 6 }$

$\\ \implies \sf \dfrac{ 10000 \times 9 \times 5}{ 5 \times 5 \times 5 \times 6 \times 6 }$

$\\ \implies \sf \dfrac{ 10000 \times 9 }{ 5 \times 5 \times 6 \times 6 }$

$\\ \implies \sf \dfrac{ 2000 \times 9 }{ 5 \times 6 \times 6 }$

$\\ \implies \sf \dfrac{ 400 \times 3 }{ 2 \times 6 }$

$\\ \implies \sf \dfrac{ 200 \times 3 }{ 6 }$

$\\ \implies \sf \dfrac{ 200 \times 1 }{ 2 }$

$\\ { \green{ \underline{\boxed {\implies {\sf 100}}}}}$

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