Question

Hi please i nedd help with these questions .

Please show workings :
1.
`(18m^2u)/(16n^3v^2) / (24m)/(15nu^3) *(8n^2v^3)/(30m^3u) \\\\`
2.
`(24a^2b^3c)/(9bc^3) / (4a^5bc^3)/(27a^3b^2c)`

Answer 1

Solutions :

1.
`\bf (18m^2u)/(16n^3v^2) / (24m)/(15nu^3) *(8n^2v^3)/(30m^3u) \\`

`\tt : \implies (18m^2u)/(16n^3v^2) * (15nu^3)/(24m) *(8n^2v^3)/(30m^3u)`

`\tt : \implies (18* m* m * u)/(16* n* n * n * v* v) * (15* n* u* u * u)/(24* m) *(8* n* n * v* v * v)/(30* m* m * m * u)`

`\tt : \implies (18* \cancel m* \cancel m * \cancel u)/(16* \cancel n* \cancel n * \cancel n * \cancel v* \cancel v) * (15* \cancel n* u* u * u)/(24* \cancel m) *(8* \cancel n* \cancel n * \cancel v* \cancel v * v)/(30* \cancel m* m * m * \cancel u)`

`\tt : \implies (18)/(16) * (15* u* u * u)/(24) *(8* v)/(30* m * m)`

`\tt : \implies \cancel{(18)/(16)} * \frac{\cancel{15}* u* u * u}{\cancel{24}} *\frac{\cancel{8}* v}{\cancel{30}* m * m}`

`\tt : \implies (9)/(8) * (1* u* u * u)/(3) *(1* v)/(2* m * m)`

`\tt : \implies \frac{\cancel{9}}{8} * \frac{u^3}{\cancel{3}} *(v)/(2m^2)`

`\tt : \implies (3)/(8) * u^3 *(v)/(2m^2)`

`\tt : \implies (3* u^3* v)/(8* 2m^2)`

`\tt : \implies (3u^3v)/(16m^2)\\`

`\boxed{\bf Hence, \: answer \: is (3u^3v)/(16m^2)}`

________________________________

2.
`\bf (24a^2b^3c)/(9bc^3) / (4a^5bc^3)/(27a^3b^2c)\\`

`\tt : \implies (24a^2b^3c)/(9bc^3) * (27a^3b^2c)/(4a^5bc^3)`

`\tt : \implies (24* a* a * b* b* b* c)/(9* b* c* c* c) * (27* a* a* a* b* b* c)/(4* a* a* a* a* a* b* c* c* c)`

`\tt : \implies (24* \cancel a* \cancel a * \cancel b* \cancel b* b* \cancel c)/(9* \cancel b* \cancel c* c* c) * (27* \cancel a* \cancel a* \cancel a* b* b* \cancel c)/(4* \cancel a* \cancel a* \cancel a* \cancel a* \cancel a* \cancel b* \cancel c* c* c)`

`\tt : \implies \frac{\cancel{24}* b}{\cancel{9}* c* c} * \frac{\cancel{27}* b* b}{\cancel{4}* c* c}`

`\tt : \implies (6* b)/(1* c* c) * (3* b* b)/(1* c* c)`

`\tt : \implies (6b)/(c^2) * (3b^2)/(c^2)`

`\tt : \implies (6b* 3b^2)/(c^2* c^2)`

`\tt : \implies (18b^3)/(c^4)\\`

`\boxed{\bf Hence, \: answer \: is (18b^3)/(c^4)}`

Answer 2

Explanation:

#1:

`(18m^2u)/(16n^3v^2) / (24m)/(15nu^3)*(8n^2v^3)/(30m^3u)`

division sign means that we flip the fraction

`(18m^2u)/(16n^3v^2) * (15nu^3)/(24m)*(8n^2v^3)/(30m^3u)`

now we can multiply all the constants together and all variables

`m: (m^2)/(m*m^4) = (m^2)/(m^4) = 1/(m^2)\\u: (u * u^3)/(u) = (u^4)/(u) = u^3\\n: (n*n^2)/(n^3) = 1\\v: (v^3) / (v^2) = v\\(18*15*8)/(16*24*30) = (3)/(16)`

now we can combine all the parts

`(3u^3v)/(16m^2)`

#2:

`(24a^2b^3c)/(9bc^3)/(4a^5bc^3)/(27a^3b^2c)`

`(24a^2b^3c)/(9bc^3)*(27a^3b^2c)/(4a^5bc^3)`

`a: (a^2 * a^3)/(a^5) = 1\\b: (b^3 *b^2)/(b*b) = b^3\\c: (c*c)/(c^3*c^3)= 1/(c^4)\\(24*27)/(9*4)= 18`

`(18b^3)/(c^4)`